New crafter with questions about cross class skills

[Frizze]

but I don't really have an interest in grinding out 15 levels of 6 or 7 other jobs.

This isnt nearly as much of a "grind" as you think it is. You can knock out 15 levels really quick. The easy way is to use the bonus exp you get for crafting an item for the first time(use all the bonus exp you can because most of them do stack - fc actions, manuals, food bonus, rested bonus, equipment bonuses). The guild supplier for each guild sells all the mats you need to make each item up to about level 15(CUL is the exception, their merchant doesnt stock fish - theres a fishmonger elsewhere in Limsa who has this covered). So you unlock the class, go stand by the supplier, work through one of each item(stopping for class quests is fine and will give you enough shards to make all these crafts plus some extra), and in like 30-45ish mins youll be level 15.