All of which is irrelevant to the request to give strength based warriors an effective distance attack. (one based off strength and not dexterity)
Have you actually played Battlemaster? A properly built Battlemaster, in most cases has 14-16 STR and 14-16 Dex. followed by a high CON. As such, you already have an effective distance attack
, it's called Pushing Attack, one for Melee and one for ranged (coupled with a heavy crossbow). Hello? Yeah, that is all we need, more backline
fighters/Battlemasters playing ranged verses their true roles, to front line and wreck stuff.........