Check some other corps, last year or so SoE has largely been in the ~1500 isk/lp range, currently they are a bit above that but I don’t know if that will hold. Some amarr corps offer a 5 run bpc Imperial Navy Energized Adaptive Nano Membrane Blueprint, that has been trading around 2000 isk/lp. I don’t know what the best corp to run for those is, been a while since I looked. you can use this to search for the corps that offer it LP Store - Return on ISK
That said SoE might be a better long run choice as the Lanngisi agent has good spawns, and that is important if you want to run burner missions. but many missions are vs angels and that is where the mach shines. You could run the apanake agent to build standings and get blood raider spawns for most missions.
There is also the option to do both, amarr + SoE storylines will balance your faction standings pretty well for the major empires.
you are spot on with blitzing. The LP is typically the most valuable thing when running most missions, so it makes sense to run them as fast as possible to max LP gains.
And you are on the right track with burners, pretty much npc’s that cheat, but can be taken down with special fits. There’s a frig version for each major pirate factions where you face a single faction frig, each of the major empire factions have a version with an assult frigate and two logi frigs, For these missions you are limited to a frigate. and then there are a handful of burner bases which have mulitple frigs (angels), or BCs (serpentis), cruiser with 2 support frigs (blood), or even a super carrier (guristas), and for these you can use maily faction or t2 cruisers, t1 bc are allowed but not typically used. with access to t2 small/medium guns and faction ships alphas should be able to do some of them, but if you can afford the setups you can probably afford to go omega I haven’t done a lot of testing there.
this thread has a video playlist
in the googledocs link and another in the comments https://forums.eveonline.com/t/blitz-and-burner-guide-v1-2-3/ and this thread has a bunch of fittings https://forums.eveonline.com/t/burner-mission-ship-advice-to-solo-them-including-fittings/