Need help with sagging mattress, fitted sheets

I replaced my 15 year old latex mattress a few months ago. My previous mattress had an 6 in med dunlop base and 2 3" 23 ILD and 19 ILD toppers. It was great but was at the end of it’s life:(
My new mattress I bought locally, has a 3" firm layer on the bottom, 3" medium in the middle and a 3" soft layer on top.
Overall its firmer than my old mattress but I sleep well on it. I have added a softer 3" topper and now it feels perfect. It measures about 13" thick.
My problem is that even with 15 inch deep fitted sheets the sheets are very tight and actually lift the corners of the mattress, so it sags in the middle.
Partly cosmetic problem but it can’t be good for a mattress to bend like this on the sides.
I never had a problem like this with my old mattress, but it had more structure with a 6" med firm base layer. It was heavy but it stayed together in the mattress cover.
When you lift the mattress up to readjust it, the mattress cover kind of dissolves into a bag filled with visible layers, it has NO structure. It is a heavy duty wool and cotton cover with a zipper.
Not sure where to go from here? I think the combo of the tight fitted sheet and the lack of structure is causing the sagging.
I think my options are to replace the bottom layer with a 6" base or find a fitted sheet with a greater depth that still fits snugly.
I’ve attached the specifications for my new mattress. I bought it from a local Bedtech factory. They are getting out of latex, it was a closeout with no warranty as they no longer carry any latex
I would appreciate your thoughts.