oh i thought you were getting new wheels.
yes a new bigger volume tyre is well worth trying. choose something with strong sidewall, not dualply if you ride uphill though!
the only time i’ve really had trouble with pinches was a worn out tyre in Afan that stretched (imagine a rubbery balloon, you press one place, the rest gets bigger, making it very easy to pinch flat). new tyre, no problems.
is your tyre worn? can you run your current rim tubeless? 21mm internal is not much different to a flow, it’s not really narrow.