In a pinch, working far from home in a church, I had to deal with a crummy spinet. The right pedal had chewed itself against the pin, which got loose and fell out. The hole in the pedal was wildly oversized, and gritty metal dust was all over the floor of the piano.
I put some five minute epoxy into the oversized hole, and some more on the middle of the pedal pin. Stuck it in, wiped away the excess on the far side.
It appears to have worked, for a long time, but for a "real" instrument, I wouldn't advise it.
If you can't get a fluted pin, you might put the round rod (ground to length with the ends smoothed) onto something metal and well supported to act like an anvil. Hold the end of the pin with vise grips. Take a hammer and give the middle a good whack. Rotate the pin somewhat, do it again. See if it then needs a little urging from a hammer to get it into the hole. Add a little CA glue once it is where you want it? Wicks in very easily.
P.S. Attempt to get it right the first time ...
You're very welcome. Glad it worked for you, with relatively little fuss. If you have to take it out and it is a little bit loose going back in, no doubt you could give it a couple more whacks.