a lot of bearing/seal shops have generic standard diameter bronze/brass flanged bushings in stock which could easily be trimmed to fit your application.
as an example, these are plastic but bronze/brass is also available. plastic would be easy to work with. the hole in the existing push rod could be made slightly larger if required I suppose. would just need a few dimensions.
https://www.mcmaster.com/flanged-bus...eeve-bearings/
https://www.mcmaster.com/flanged-bushings/
https://www.motionindustries.com/tax...ings/browse/en