I don't know of a real workaround, but for the Resort Shirakami (or any rapid train rather than limited express), it's probably easiest to just buy and pay for the seat reservation, 330 or 530 yen depending on the date. Just check the "Purchase tickets such as the Super (Limited) Express Train ticket only" box.
I've done it for the Resort Shirakami and High Rail 1375 (plus others in West Japan) and imo it's worth it, especially around any holiday when those two and some others sell out way in advance.
At the risk of sounding cheap but I promise I am just interested in the technicalities: Would it be possible to buy the seat reservation (to guarantee a seat) and then some time later (but well before the Joyful Train departs) present oneself at the ticket counter armed with the JR Pass to get a refund of the seat cost while keeping/transferring the seat under the JR pass? My reading of the JR East website suggests that seat reservation fees are mostly refundable if canceled more than a day in advance but sometimes the translated information does not always match with reality.