That GXV140 air cleaner is the same as mine (there have been two designs, the side-mount and the top-mount), but I've never seen that sheet of foam between the filter and the housing. I'd better take another look - if I can put one in, that engine's last bad feature (apart from the plastic camshaft) will disappear. Well, I don't like the starter either - compared with the GXV120 and GXV160 starters, it's a bit tin-pot.
At $50 for that HRU214 self-propelled, you seem to have bought the bargain of the year roebuck. Last week I bought a bare engine from an HR214 self-propelled (early version of the same mower) for $20, and ended up having to throw away all of the major parts due to terminal wear. I got the bits I needed (complete air cleaner, throttle links, carburetor insulator, fuel cap, fuel filler-neck grommet) plus a carburetor and an ignition module for spares, but everything else went in the garbage. I'd been trying to find an air cleaner for a long time, and got desperate.
I don't like the GXV160 much - according to the manual it's 3 kg (26%) heavier than the GXV140 and only has 0.5 hp more power. No Honda mower engine is light, but another 3 kg is just what they didn't need (especially when you're lifting one onto the bench). I understand the GXV160 only began to sell in meaningful numbers after the GXV140 went out of production, which according to Wikipedia, happened in 2001:
http://en.wikipedia.org/wiki/List_of_Honda_engines
