You could try constructing the target URL inside the rewrite conditions:
RewriteCond ##%{QUERY_STRING} (.*)##(|.*&)param1=([^&]+)
RewriteCond %1/%3##%{QUERY_STRING} (.*)##(|.*&)param2=([^&]+)
RewriteCond %1/%3##%{QUERY_STRING} (.*)##(|.*&)param3=([^&]+)
RewriteCond %1/%3##%{QUERY_STRING} (.*)##(|.*&)param4=([^&]+)
RewriteCond %1/%3##%{QUERY_STRING} (.*)##(|.*&)param5=([^&]+)
RewriteCond %1/%3##%{QUERY_STRING} (.*)##(|.*&)param6=([^&]+)
RewriteRule ^foo$ /bar%1/%3? [L,R]
When I try to request:
/foo?param1=a¶m2=b¶m6=3¶m3=4¶m5=5¶m4=6
I get redirected to:
/bar/a/b/4/6/5/3
Adding any additional required query string parameters won’t make it look any more messy than it already is.