My antenna is copper, elements and the beam. I would like to bolt them together where they cross. Would stainless bolts work? Just sweating them together lets them twist and move some in high winds.
Stainless steel fasteners, lead and tin are compatible with copper. Lead tin solder, however, has poor mechanical strength as you have apparently discovered. Solder can be used to improve conductivity and moisture ingress and is best when used with other mechanical strengthening measures. So the use of stainless fasteners to improve the mechanical strength of your antenna is practical.
Avoid the use of aluminum or zinc fasteners with copper as these will cause the fastener to deteriorate through the mechanism of galvanic corrosion. If a copper wire must be directly attached to a galvanized metal such as tower leg, a stainless steel shim can be placed between them to avoid the galvanic corrosion since stainless steel is compatible with both materials.