6/2 copper is too costly, it would be a mistake to use it. You are correct it won't fit on a receptacle. It may not fit on a 20A breaker either. *Since you've got that problem anyway, you might as well add a fused disconnect or subpanel simply to serve as an adapter from large wire to small. (the fusing to allow you to use a larger breaker that takes larger wire). And once you've done that, you might as well switch to aluminum wire as well.
Your pump needs a 20A circuit because 13.8A x 125% = more than 15.
The first strategy is to replace the pump with a 240V pump because it's cheaper than heavy wire. At 240V, this isn't even hard - just 2% drop on 12 AWG wire. The price difference between #12 and #6 (even aluminum) will probably pay for the pump. If it's a plug-in temporary pump, time to get serious and hardwire in a proper pump.
If you really want 120V out there for other reasons, then feel free to install, say, 2-2-2-4 aluminum or even 2-2-4 (120V-only) to a subpanel. #2 will typically fit on a 60A breaker, so use a 60A in the main panel and circuit-appropriate breakers at the disconnect or subpanel. They won't make a 60A/120V breaker, so use a 60A/240V and only attach to one leg.
and maybe an option that would be sensible where voltage drop code is a bit more lax.
Other than switching to a 240V pump, your best bet is to secede from Canada and join the United States. Here we don't care about voltage drop, as long as it doesn't interfere with fault clearing (the breaker tripping on a dead short)... so there's about a 10% practical upper limit on permissible drop in the US. In Canada it must be <=3% at either 100% of the actual load or 80% of the breaker if it's a general-use circuit or feeder.