A recirc would guarantee that the short bursts by the washer would be hot but it would still be short-cycling the tankless, so the heater's efficiency during those fills would still be at most 60%. That's not exactly a problem, since the volumes on high-efficiency washers are small. A 20-30% hit in efficiency on a small draw won't be easy to measure on the fuel bill- it's the big volumes like tub-fills and showers that make the largest difference.
Takagi's have been used with recircs for years- they recommend limiting the recirculation flows to ~ 2gpm flows to minimize wear on the heater. But since you're not running it 24 hours/day it won't much affect the longevity for you even if it's 6-8gpm. If the total volume in the loop is less than 5 gallons it's a bit of an efficiency hit on cold starts but not a huge one during maintenance burns, and would not have a measurable effect on the fuel bill (it's only measurable in the lab, but it's something to note if max-efficiency is your stated goal.)
If you insulate the loop to R4+ (3/4" wall or more closed cell foam) odds are good the recirculator will only run once per on-period at the beginning, and only rarely as a temperature maintenance burn.
If the difference in installed cost between an 0.82-0.84EF Noritz/Rinnai/Takagi and a 90%+ condensing unit is $1000 or more, if your family normally showers rather than takes tub baths you will get a better return on investment (and use less fuel) installing a drainwater heat recovery system that returns 50%+ of the drainwater heat to the incoming cold water. (Not always easy to install, if the heater isn't already close to a drain downstream of the showers.) Natural Resources Canada maintains a list of third-party tested drainwater heat exchangers by effieciency here. There may be provincial & federal subsidy for installing one too. (I'm not sure what B.C. offers relative to other provinces.) Drainwater heat recovery extends the apparent capacity of tanks during showers too- it's like having another ~30KBTU of burner (that uses no fuel). It does nothing for tub fills however- the drain and potable have to flow simultaneously for the heat exchange to take place.
There's more to moving from a 50gallon tank to a tankless than the cost of the unit- in many/most installations the gas plumbing has to be upgraded to support the much larger burner, and for non-condensing units the cost of venting can be substantial if it has to go any distance. Get some quotes.