What can be used instead of cheese to help a grilled sandwich stay together?
If you find roasted sweet potato to be a strong flavour, that makes things harder. Mixed roast vegetables, including some roast sweet potato or squash can work well, and the flavour of one vegetable doesn't dominate. 

A rather thick hummus is also good (it softens a little on warming). In fact, roast veg and hummus is probably the vegan panini I see the most. Peanut butter should work, but I find that when heated it can become unpleasantly sticky (depending on brand; other nut butters that start stiffer may be better).

All these options have their own flavour, but so does cheese, even if very mild. The trick is to work with it, not against it.