Akrober3,
I’m not sure how relaxed your work environment is but, I would just be upfront and ask as well. Schedule a one on one and roll all these questions into a performance review. If you get the sense they like your abilities and you as person, be all means tell them that you like the company and are highly interested in staying on full-time. If there is some hesitation on their part, probably a good idea move forward with plan b and c. Good luck man!