Never buy cheap tips. Tips are The Thing. Everything else in the iron is just there to drive the tip. You are soldering with the tip, not the rest of it (unless you have a very strange technique!).
So... throw them away, and get a new tip from Hakko or someone who can be trusted to sell genuine Hakko rather than the many counterfeits available. Hakko tips directly from Hakko's website are not very expensive.
Then... I'm wondering if your technique over the years is based on irons that are too hot, and you're just used to it. 750F is too hot for most normal soldering. I might suggest 650F or so, except on special occasions where the components are more massive. If it's taking legitimately too long to heat up the parts, and all other issues have been properly addressed, turn up the heat a little, temporarily. Nothing in your list of typical connections strikes me as being very massive, so in general, ... no.
I wonder about cleanliness; oxides and such can be horribly detrimental to good heat flow. I wonder about the solder you're using; if it's, well... cheap... it could have bad flux or other contaminating ickiness that's just making a mess of everything.
I don't know which tips you're using, but the mass between the heating element and the workpiece, i.e. the mass of the tip, makes a pretty huge difference in the heat transfer. It could be you're not using the right one. I like chisels, and I choose them to fit the size of the connections I'm working on. For "normal" stuff, probably a D16 or D24.
Good temperature control, good tip, good solder, good flux, good technique, and you should be soldering up shiny trinkets like a ninja! I really don't guess it's the Hakko; several other factors have changed, no? Take one issue at a time and make sure you've got it covered, then move on.