Toro mower raising handle bar

[Tiger Small Engine]

Is it possible for you to make an adapter plate that will attach to the existing mounting & let you connect the handle at an angle you like?
Electrical junction box covers provide inexpensive, flat steel if you need a couple of small pieces for the job.

It isn’t uncommon for mowers to develop slop in the push handlebars over time. Without welding and modification, there isn’t much you can do.