No one has mentioned that the brake controller/brake systems may cause tire problems by locking up the wheels, but with two blowouts in a short time you should eliminate that as a possible source of the problem.
I whole heartedly endorse this recommendation. We got several years out of the stock Ranier tires (don't recommend them as a replacement however) that came with the trailer. But early this year we were turning left off of a small two lane highway and a guy at the stop sign on the road we were turning on started honking his horn.
We stopped and rolled down the window to talk to him and he said there was smoke coming from the tires as we braked to slow down and turn. At the time I had no idea that the brakes were not self adjusting.
I pulled over and sure enough I had several almost bald spots on my tires. So I re-adjusted my brake controller settings and fortunately we were reasonably close to home and were able to get there without incident.
So in addition to new tires we also had the brakes adjusted by a nearby RV dealer with a good reputation.
While your tires were definitely too old, I can't help but speculate that your trailer brakes locking up may be a contributor to the blowouts. So with new tires, you also need to adjust your brakes, and depending on use, do this every year or so and probably a good idea to do that along with an annual wheel bearing repack.
For tires, we went with Caryle. It seems (my guess here) that about a third of Escape owners buy Caryle and about 2/3 seem to prefer Endurance. You can go with the stock tire brand Ranier, but almost everyone on the forum seems to universally dislikes the brand. We were getting ready to list our trailer for sale and I (unlike your seller apparently) could not conscience putting Raniers on the trailer even though it would have saved us $100+ or so. We are switching to a 21C and the last thing I want is to see the buyer of our 19 at the next rally and have them cuss me out for putting cheap tires on it. Even before the brake adjustment issue, the Raniers seemed to wear pretty fast.
The Caryle tires I purchased at Amazon were delivered promptly and the date on the tires was earlier this year, so they were less than 6 months old and had not been sitting in a warehouse somewhere for years dry-rotting. I also used Amazon Prime and verified that these tires had a "free return", which I would have used if they were more than a year old. We had them installed at a local Firestone dealer. I had to remove them myself and it took two trips to Firestone (I could only jack up one side at a time), but they were very accommodating even though it took the better part of a day. If you don't want to remove them yourself, I'd ask the tire dealer if they will do it for you if you tow the trailer in.
Here is the link for the tires I purchased:
https://www.amazon.com/gp/product/B01IHIMKFE/ref=ppx_yo_dt_b_asin_title_o08_s00?ie=UTF8&psc=1
Wish you the best on getting new tires, but for your safety please do not ignore having the brakes adjusted.
