John,
The FP back plate fits the LA engines, so yes the LA gasket will work. I use FP back plates on all my LA engines, instead of those cheap plastic factory back plates that often leak.
Gaskets are very easy to make, if you can't find a source.
I like to clean the case, and glue a slightly oversize piece of gasket material directly to the case with low tack adhesive such as rubber cement. When the adhesive is dry, use an Exacto #11 blade to cut around the inner diameter of the case opening, being careful to keep the blade parallel with the inside surface of the back plate opening, and cutting on the down stroke only (so you don't pull the gasket material away from the case).
Punch the screw holes out, and bolt the back plate inside out (backwards), to the engine crankcase, with the partially cut gasket in place. This makes cutting around the outside edge of the gasket much easier, but if your careful you can cut the outside edge without this step.
Much easier yet, is to simply clean the case and back plate with Acetone, or any other suitable grease solvent. Apply a very thin coat of RTV high temperature silicon adhesive (red) around the mating surface of the case, being sure to keep it from being squeezed down into the case. Now apply an equally thin coat around the inside flange of the back plate, and mount the back plate on the engine in the normal position. The RTV takes about 72 hours to cure completely, so don't get anxious to run the engine before then.
One advantage of the RTV seal, is that it's thinner than a gasket, and in effect provides a small amount of crankcase stuffing. Be sure to check crank pin clearance first, by installing the back plate dry, and sliding the crankshaft aft to it's limits while rotating it by hand to be sure the crank pin does not contact the backplate without a gasket acting as a spacer.
Sorry for the long winded reply,
Bill