I agree shot string does not mean longer will not pattern well on a plate and kill Dove just fine, but I do not like slow loads given a choice. I worry more about pressures. SAAMI .410 3" max. is 13,500. Based on Winchester Super X HS 3/4 ounce loads pressures run 13,100-13,500 PSI with velocity of 1100 FPS. Same hull with 11/16 ounces shot can not reach 1200 FPS without pressures reaching near max as well. You can drive 5/8 ounce shot slightly above 1250 FPS at slightly under max pressures but that load is lighter than you want.
Then the question is what will a larger volume hull give you? More room for sure, but is that going to be enough? You may need a slightly wider wad to seal the hull so you do not get blow-by. So no PC orange as they are the smallest diameter, followed by Remington, Federal and then old AA and new HSAA. I would start with the HSAA. Do not know off hand about some of the Euro wads, but in general they do run wider to seal straight wall hulls better. Hard enough shot should be OK without a full shot cup to protect it. You might get 3/4 plus, maybe 13/16 ounce to fit. But can you get velocity and keep pressures in line? After that how do they pattern?
Only way to know is load some and have them tested for pressure and velocity. It will need to be 300MP. I have found LilGun, 410 and 296/H110 loads run higher pressures than 300MP, by a lot. I do not know the pressure curve and how quickly it climbs. But you can load 3" Remington hulls with 11/16 to 1200 fps at 9000PSI with 300MP, Lil Gun will be 1175/13,500 range, 296 will 1135/12,800. So that should give you a starting powder and range of loads to work with. You could also look at 4227, 2400, Herco, Unique or 452AA none of which would be my first choice for various reasons.
The other question is what will be the difference in pressures between a brass hull and a plastic hull? Brass will not flex as much so will that increase pressures? Again the only way to know is load and test some. Also what type primers will you be shooting? That will alter pressures a lot. Do you plan on using a large rifle primer? I did read one report about wad sizes and cards to compensate for wad lack of good seal. "Whenever assembling metallic .410s with plastic shotcups an over-powder card MUST be used. This is necessary because the plastic shot cup diameter is too small to seal the interior case wall, such that omitting the over-powder card results in powder leaking past the wad, causing “bloopers.” " Again start with HSAA and you might not need a over the powder card.
