Looking at companies that offer to print and laminate books you can find out what typical paper stocks are used.
For example the site printabook.ca mentions:
300gsm art stock (option for gloss or matt laminate to increase durability)
The site printninja.com gives a comparison of the different kinds of paper used:
The lightest cover stock we offer, 10pt. cover is a great fit for catalog covers, and is often the best choice for the cover of any perfect bound project 6″ x 9″ or smaller. (250 GSM metric weight)
A medium weight cover stock often used as the cover paper for trade paperbacks, graphic novels, and many perfect bound projects larger than 6″ x 9″. (300 GSM metric weight)
The heaviest cover stock we offer, 14pt. cover gives a rugged, durable feel and is often used for any project that will be handled a lot, for very thick perfect bound projects of any variety such as catalogs or graphic novels, or for oversized projects larger than 8.5″ x 11″. (350 GSM metric weight)
This shows that you are using the perfect type of paper for very large books that are handled very often. If you are looking more for something that you would usually find in a bookstore it looks like 300 GSM would be better instead of the 350 GSM you are currently using.
270gsm laminated cover stock
That is quite close to the other suggestions of 300GSM.
All in all it looks like 350 GSM is simply too much for most average projects, so you might want to try something in the range of 300 GSM.