You are right to be "fussy" but the only thing I would say is...
A song with a "small fry" publisher is better than a song sitting on your PC doing nothing
Unless you are being inundated with publishing deals I would be a little more positive with the publisher and rather than asking about past succes (a new publisher may not have a track record - but all publishers started somewhere) I would ask more about what they would do with your song and what contacts they have
Even though the publisher may be small fry the person setting it up may have worked for one of the big boys and have lots of contacts
When an offer comes in it is difficult deciding whether it is right for you and you probably think tying your song up will mean you will miss out on the next multi-million pound deal
How likely is this though?
How hard are you pushing and to who - how many publishers haven't come back to you?
I would say the following proverb could help:
A bird in the hand is worth two in the bush
You could consider just signing this single song with the publisher (or ask for a non-exclusive deal a although this may not be attractive to your existing publisher and future ones you pitch to)
If you sign this song you will then be a "published" writer when you pitch your next songs so you could simply use this deal to increase your credentials for future deals/pitching