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Epoxy resin would be better. You could try to just get back to the core and add a new wooden surround using epoxy resin. That would be a good combination of durability vs price.
Alternatively cut the bottom off and replace with a solid piece of pine, or some pieced together. Joined with dowels and epoxy.
Repaircare is a good epoxy to look at. They have a lot of examples on their site.
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which the previous owner ignored by sticking some mitred skirting around them.
Are you 100% that the skirting isn't there to prevent water getting into the gap between the post and the concrete surround?
You're inevitably going to get shrinking/expansion in the wooden post creating a gap for water to get in.
It's obviously not worked perfectly, but if it's still solid and it's been there a long time it's worked well enough.
I'd go the epoxy route for the wood and then find some sort of flexible product to fill the gap and then add some form of skirting to help limit water ingress - even if its more the size of scotia beading instead of full skirting.
On the point of it just being kicking it down the road, I'd have thought if you do a good job and keep an eye on it you'd get at least another 5yrs out of it. At which point you'll have more, and larger blocks of free time as your kid(s) will be older and you won't have all the other house bits to contend with. Propping and replacing wood sounds like an uninterrupted weekends worth of work vs something you could do in a series of 30min to 1hr blocks over multiple days.
Attentions now turn to the porch. The worst parts are the bases of the two uprights, which the previous owner ignored by sticking some mitred skirting around them. The porch as a whole feels solid, there's no movement, so I'm sure there's a core of decent wood in there. Question is what to do? Remove loose bits, wood hardener then build out with filler, sand and paint?
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