Your current 700c wheels sound like entry to mid level. If they don’t have tons of miles on them I’d suggest waiting until you get the new tires to see how happy you are. That’s a good choice and I would have suggested quality new tires first before anything else. If you’re happy with the ride then all is good. If you’re not putting too high a demand on the wheelset, the biggest thing you might run across is shorter lifespan with cheaper bearings, etc.
If you decide on new wheels, a Shimano 105 (or older Ultegra/600) on Open Pro rims will give you many years of quality riding.
BTW, what brake set are you using? The 27” to 700c conversion with canti brakes can often be a challenge and viewers want to know!
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N = '96 Colnago C40, '04 Wilier Alpe D'Huez, '10 Colnago EPS, '85 Merckx Pro, '89 Merckx Century, '86 Tommasini Professional, '04 Teschner Aero FX Pro, '05 Alan Carbon Cross, '86 De Rosa Professional, '82 Colnago Super, '95 Gios Compact Pro, '95 Carrera Zeus, '84 Basso Gap, ‘89 Cinelli Supercorsa, ‘83 Bianchi Specialissima, ‘VO Randonneur, Ritchey Breakaway Steel, '84 Paletti Super Prestige, Heron Randonneur