If it's a common item with a listed price, and you're in a city big enough to reasonably have that item in stock, just do your shopping "offline". Sometimes I even include a low-level Forge cleric in small towns so the party could do their sub-100gp item shopping. (In that case the cleric charges an extra 10% donation for the Forgetemple, which they will use to feed orphans, create farming equipment, etc...)
Yeah, the story setup makes it seem like your mission is actually urgent, so I also only long rest when it's absolutely necessary.