Is there a recommended maximum safe number of products?

Hello. We are creating a WordPress multisite store for a client. Each subsite will be mapped to a separate domain. We have activated MarketPress at the subsite level (not Network Activate). We have set Stripe payments and FedEx and UPS shipping info per subsite, though they all use the same credentials.

This is our second build of this network. A month ago, we had a perfectly functioning network of sites and were ready to deliver it to the client. Our final task was to upload the remaining products for sale. When we crossed about 2,000 products per site, we started noticing quirky behavior in MarketPress. The site began running slowly, Store Settings needed to be reset periodically, the Orders admin sometimes did not display orders or portions of orders, out of stock products would display even though they were set not to, and checkout would not always complete successfully. Eventually, all of the subsites became completely dysfunctional and we had to rebuild from scratch.

You can bet that our second installation of this project was built with extreme care and documentation.

Now that we are within days of delivering this long overdue project to our more-than-patient client, we began filling his store with products. Much to our horror, we are seeing the same dysfunction returning to our painstakingly rebuilt network. The subsites that have a full complement of 5,000 products are displaying out of stock products even though they are set not to, the Billing/Shipping Address accordion on the checkout page opens and closes randomly while the user is trying to fill it out. But more importantly, these sites will not render an order status page or mp-create-account-lightbox at checkout. The orders are being placed, but the user has no way of knowing that by looking at the screen that just shows an infinitely spinning icon.

Is it possible that MP has a critical mass threshold for the number of products it can handle? Please share with us your recommendations or guidelines for how many products and images it is safe to upload for optimum performance.

The subsites that will no longer checkout properly, and have more than 3,500 products are:
https://001.amazingwholesalejewelry.net
https://002.amazingwholesalejewelry.net
https://005.amazingwholesalejewelry.net

The subsites that will checkout properly, though slowly, and have less than 2,000 products are:
https://004.amazingwholesalejewelry.net
https://006.amazingwholesalejewelry.net
https://007.amazingwholesalejewelry.net

The subsites that work the best, and have less than 800 products are:
https://011.amazingwholesalejewelry.net
https://012.amazingwholesalejewelry.net

I have screenshots of the errors I see after clicking the Submit Now button at checkout.

Thank you in advance for your help.

Mihal
(Ehventerprise LLC)