You didn’t shock your yeast by simply moving it to a room that was 65°. The thermal mass of 5gal of ACTIVE fermenting wort is pretty substantial so it would have taken a long tine for the temps to come down. At 1.052 and upper 70° likely the beer had fermented out. This was exacerbated by adding additional yeast into a warm environment. It will be beer but here are some tips for your next batch:
1) try to acclimate your rehydrated yeast by adding small amounts of cooled wort. This will help with the initial temp shock. Also, do NOT rehydrate with RO or distilled water.
2) 36 hours is the upper limit you want to see in terms of lag. Every hour that passes allows wild yeast to take hold. No matter how effective you sanitize you will have wild yeast in the wort. Everyone does. Pitching an appropriate sized, healthy yeast population overcomes this issue.
3) adding yeast to already fermenting beer is a waste; you won’t get much at all. A hydrometer meter is worth its weight in gold. Not only to find out when it’s finished fermenting but also if it has started.
4) sounds like you understand some portions of temp control. Remember that fermentation is exothermic (produces heat). This means temps will easily climb 4°-5° over ambient, for a beer that is 1.050-1.060. I just made a DIPA at 1.075 and it easily climbed 6° over my ambient. My glycol system ran quiet frequently to keep it at 67°.
5) I’ve found that trying to “fix” beers with too many changes at once usually causes more issues and can ruin the beer. If you have to try one change at a time (I.e warming it a bit, then trying another fix if it doesn’t work). Sometimes you just gotta let it ride!
Do t give up. Brew another beer and get comfortable with the process and good technique to make good beer. It will come.