I've decided I probably won't experiment with killing POSes for now as my friends aren't really ready for it. We're going to find our feet doing pvp roams in T1 frigates and cruisers before we take on anything too advanced. I do think I could solo a lot of POSes but I wouldn't beat what most people can bring to the timer solo.
I'm going to explain why I could (or anyone can) solo many POSes by looking at the POS modules that can function at extreme range. There's not many.
Part of this is due to the odd POS mechanics. A POS defensive module is sited outside the POS shield (except for hardeners which modify the tower). However the range of the module is measured from the tower. This means that if you have a correct sniping perch you can shoot a module at 250 km which is still at least 35 km from the tower and your perch is actually 285km from the tower. Ravens, Nagas, and Apocs can all shoot POS modules while effectively outside the 250km range. This makes Energy neut batteries, which have precisely 250 km range, useless against a properly placed POS sniping fleet.
In addition range modifiers effect gun batteries and pretty much every site recommends high damage close range ammo like EMP or Fusion.
Here are the effective ranges of POS defensive modules measured from the tower. Bear in mind our fleet will be at least 285 km away. I'm assuming that modules are matched to the towers that give bonuses to them.
Amarr Control Tower
50% bonus to Energy Sentry Optimal Range
25% bonus to Energy Sentry Damage
Frequency crystals have a -50% range bonus with close range high damage ammo, 60% range bonus with long range ammo
Large Beam Laser 562.5km optimal, 100 km falloff
Medium Beam Laser 420.75km optimal, 75km falloff
Small Beam Laser 281.25 km optimal, 50 km falloff
Large Pulse Laser 159.75km optimal, 28km falloff
Medium Pulse Laser 119.25km optimal, 21 km falloff
Small Pulse Laser 78.75km optimal, 14km falloff
Caldari Control Tower
25% bonus to Missile Battery Rate of Fire
50% bonus to Missile Velocity
-75% bonus to ECM Jammer Battery Target Cycling Speed
ECM Jammer batteries 200 km optimal, 100 km falloff
Citadel Torpedo Battery 472.5km
Cruise Missile Battery 562.5 km
Torpedo Battery 168.75 km
Note: missile batteries are rarely used as defence because the batteries don't work after the tower is reinforced.
Gallente Control Tower
25% bonus to Hybrid Sentry Damage
Hybrids have a -50% range bonus with close range high damage ammo, 60% range bonus with long range ammo
Large Blaster Battery 21km optimal, 35km falloff
Medium Blaster Battery 16km optimal, 26km falloff
Small Blaster Battery 10km optimal, 17km falloff
Large Railgun Battery 300km optimal, 150 km falloff
Medium Railgun Battery 225km optimal, 112km falloff
Small Railgun Battery 150km optimal, 75km falloff
Minmatar Control Tower:
50% bonus to Projectile Sentry Optimal Range
50% bonus to Projectile Sentry Fall Off Range
25% bonus to Projectile Sentry RoF
Projectiles have a -50% range bonus with close range high damage ammo, 60% range bonus with long range ammo
Large Artillery Battery 450km optimal, 408.75km falloff
Medium Artillery Battery 420.75km optimal, 307.5km falloff
Small Artillery Battery 281.25km optimal, 210km falloff
Large Autocannon Battery 31.5km optimal, 106.875km falloff
Medium Autocannon Battery 22.5km optimal, 78.75km falloff
Small Autocannon Battery 15.75km optimal, 52.5km falloff
Not bonused by tower type:
Sensor Dampening Battery 150 km optimal, 150 km falloff
Stasis Webification Battery 150 km optimal
Warp Disruption Battery 150 km optimal
Warp Scrambling Battery 75 km optimal
Energy Neutralizing Battery 150 km optimal
So let's see: what can hit us at 285km range
Large Beam lasers with close range ammo (assuming Amarr tower)
Medium and Small Beam lasers with medium or long range ammo (assuming Amarr tower)
Large Pulse lasers with long range ammo (assuming Amarr tower)
Medium and Small Pulse lasers can't hit us
ECM jammers are 57.5% effective
Citadel and Cruise missile batteries
Torpedo batteries can't hit us.
Blaster batteries can't hit us.
Large railguns with medium or long range ammo can hit us.
Large railguns with close range ammo can just barely hit us near the limits of falloff.
Medium and small railguns with medium ammo can hit us in falloff
Medium and small rails with long range ammo can hit us.
Medium and small rails with short range ammo can't hit us.
Large and medium autocannon batteries with long range ammo can hit us in falloff (assuming Minmatar tower)
Otherwise autocannon batteries can't hit us.
Large and medium artillery batteries can hit us (in falloff if close range ammo loaded). (assuming Minmatar tower)
Small artillery batteries loaded with short range ammo can only just hit us in deep falloff (assuming Minmatar tower)
Otherwise small arty batteries can hit us (assuming Minmatar tower)
Sensor dampening batteries are 55% effective
Neuts, webs and scrams can't hit us.
Conclusion. There aren't that many defences with adequate range to defend against long range assaults, particularly as many players prefer to load close range high damage ammo. Missile batteries have ample range but are rarely used because they offline if the tower is incapped. Plus they're vulnerable to sig tanking. Many large batteries are also vulnerable to sig tanking and will be rarely used outside of nullsec because they're meant for shooting capitals. The only ewar that reaches are damps and ecm which can possibly be countered by using FoF missiles. Alteratively some alts or friends in noobships can orbit your Raven to draw ewar.
In many cases testing a POS will be a simple matter of checking if it has close range ammo loaded. If they are using short range ammo then it's only really artillery that's both commonly used and dangerous. As many towers aren't Minmatar towers with medium artillery that's a lot of towers that will be completely vulnerable to long range assault if close range ammo is used. It would be quite interesting to test afterburner Nagas maintaining traversal against artillery batteries which have a reputation for tracking poorly. In any event logistics ships could sit 50-70km behind the dps ships and be safe against most towers.
It's very simple to test whether a tower can defend itself at range. Just park an alt in a noobship at 285km and sit still. See if the tower can kill you. If it can't you're probably ok to bring in snipers.
There are also some interesting lessons for tower builders here. First, your long range defences are for long range defence - be careful not to use high damage ammo. ECMs are really good although perhaps fof missiles counter them. (Can't imagine there's many other people flying around Eve shooting towers with fofs though). You could probably make life hard for fof users by anchoring lots of secure containers in front of your defences. The bonuses really help, try to fit guns that suit your tower's bonuses. And finally if the grid is extended then an active tower defender can shoot out to ridiculous ranges - with long range ammo a large artillery battery can hit anything closer than 2028 km.