A few issues with Proving Grounds
-There needs to be at least one Health Relic within the home base itself. As it stands right now, Champion select is already punishing enough and there's very little incentive to try and fight a game where, in an all other things equal set up, that get the magical double mage, ad carry, poker, and Tank set up against your Tryndamere, Fiora, +3 other melee team.
An additional health relic location aids in the near constant siege that a mostly melee team deals with. Perhaps even moving the health relic in front of the first tower to the back of the second tower is sufficient.
Alternatively, adding to the Proving Ground Global Buff, improving item based Health Regeneration would help out heavy melee teams as well, or removing the improved Mana Regeneration (Thus requiring a bit more thought or investment in mana regeneration to continue the poke fest.)
Secondly, I personally don't approve of the "Execution" model of wrapping up a team fight. ARAM has that Iron Man kind of feel to it that you stay in as long as you possibly can only to come back even stronger; Being able to deny the experience and gold for your death and coming back being even harder to kill makes punishing team set ups even more so.
Solution? No Credit decay. Even if you ace the team and die 45 seconds afterwards, they still get credited with the EXP and gold. You can still strategically suicide if you have no health and dying in one hit in the next team fight would be very bad, or if you really want to buy, but someone's going to benefit from it.