TLDR: Grenades aren't worth it for cheesing strength. Just whack off in the dark with a bud for 14 raids. Elite Strength will take between 75-100 days of whacking off three times a day every day on top of normal play with grenades.
Strength Training has diminishing gains and levels from overweight walking, throwing grenades, and melee hits. The two cheesing methods are to throw 8 grenades which is the maximum for 129% exp (1.3 points) and/or fully exhausts melee hits with 34 whacks (3 points).
Each grenade + melee raid nets 4.3 point at 89,834 Rub cost. 40 skill points takes 9.3 raids (rounded to 10). Cutting out the 1.3 points from grenades means 13.3 raids (round to 14) but at a cost of 30,532 rub for two Salewa and two grenades. Healing costs are substantially less if using a Grizzly instead of Salewas and letting your PMC passively heal while you Scav raid.
Buy a Freeman Crowbar (2nd lowest damage melee with good range so you don't miss). If you don't have a gamma or epsilon grab a bank robber or throw fewer nades. Each person will take a minimum of 544 damage (34 hits x 16dmg) so a Grizzly or two Salewa are ideal as 800 points of heals. That leaves room for 1 RGD (10,532) + 4 Zarya (8186) with another 4 Zarya in pockets. Technically only one person needs a RGD and if you're scared of scav marked and cursed bring a pistol.
Go into a raid, ideally in off play times, at night. Shoreline, Customs, Woods are all good options. Load in, one person crouches and hits the other one's leg while they continuously heal. Switch hitters. Then at the end throw your grenades and use the RGD to suicide.
If someone comes up while you're whacking off with your bud in the dark woods just start throwing those zaryas everywhere. Grenades come out of your pockets first so you'll only have to throw 1 to 3 of them before your only risked gear is expended.
You don't need to fully heal from Therapist after suiciding. Just heal your legs as you'll be suiciding again anyway.
For those looking to cheese all the way to Elite Strength: Assuming 46 "unnatural" levels of strength and 5 naturally from playing you have 920 points to cheese. Budget whacking off plus one suicide nade is 3.1625 points for 291 raids. As an "Elite" Gamer adding whacking off three times a day every day would take you 97 days to achieve Elite strength. Even assuming 10 natural strength levels you'll still need 75 days of uninterrupted S&M sessions to hit 51 plus 6.9mil cost in Salewas + grenades.