It seems to me that your confusing a few issues let me see if i can clarify this a bit.
1. as far as the 15' screen height: during a performance limited
DRY RWY TO if an engine fails after V1 (takeoff decision speed) the minimum height that that a jet is "allowed by law" to cross the screen is 35' by that height and (by law) the speed of the aircraft must be V2 (TO safety speed), by THAT height 35'. during operations on
WETor contaminated rwy's attempting to stop at the actual V1 will probably cause you to overun the rwy, so a reduction from the DRY V1 becomes necessary. so a few knots is knocked off the dry V1 i.e. V1- 10 Kts. This decision results in a performance penalty whereby, you end up over the screen (in the worst case scenario) crossing the screen as low but NOT LOWER THAN 15' agl. However you still must reach the safety speed V2 by 35'(by law).
2. The concept you seem to be confusing is the accelerate stop with the take off distance available (ASDA
vs TODA) when determining the former in dry conditions reverse thrust is not factored in on dry RWY's but RT is allowed in determining the WET distance.
3. With all that said I've probably mixed up something and there are many here who are MUCH more qualified to respond to your query than me as I don't yet fly jets, but I'm nevertheless in love with them and don't care to much for high performance/complex or multiengined piston aircraft but those are expensive and jet training costs even more not, so easy to follow that passion. gotta stick with biochemistry and molecular bio and Piper Warriors for now.
4. Almost all questions about jets are answered by the book by David P. Davies, Handling the Big Jets Third edition (70-150$). Got mine from Australia long ago; if you're not hooked after he does 'Stalling' you need your head examined
Hope some of this helped Rhov