mg -
I haven't installed the booster yet either. I probably will at some point, but honestly & in my opinion, it's not a necessity with my short 1575 or your even shorter 1475.
When I do install it I have been thinking about inside the mounted spare tire (which is nice & dry under a 1575) or like you're thinking - somewhere around/under the A-frame tongue area.
As far as power for the booster goes - I will probably go the K-I-S-S route and just use the roach, er alligator clips on the battery posts. Quick & easy.
I would try a test tow or two without the booster and see if you lose connection.
Just my $0.02.
Glad that yours arrived. Please keep posting thoughts and updates. I will do the same (hoping to get out on a trip soon).