Ugh....So... All work performed as an LSRM can and does count towards getting your A&P via work experience, so long as it's an aircraft which has had an A/W. In other words, time spend building an aircraft doesn't count. (it used to count). It may be work on an S-LSA, E-LSA, or AB. As an LSRM, you are self-supervised. No A&P is involved. Because anyone can work on AB, that time would also count despite it being an RV14, or other non-LSA. LSRM allows you to work and inspect (cond & 100 hr) S-LSAs. It allows you to inspect e-LSAs (cond). Anyone can work on E-LSAs.
As for "type specific training"... The FAA is openly very loose with that concept...Go read the manual.