You should be fine. I need to get back there, only been back once since the late 1990's.
There was a Best Western in town & another motel with a pool and hot tub which was nice after hiking. As others said, mid-week is best. Give yourself a few days. Since you've done the NH48, after Katahdin, you may be back for Hamlin & North Brother, the other 4K peaks. (Coe, Fort & South Brother are on the NE 100 highest.)
Ponds along the way to the Brothers are great moose spots and Sandy Stream Pond, near Roaring Brook and on the way to South Turner, is almost a guarantee moose sighting. (South Turner's summit view of the Katahdin Basins made the photo credits in Forest & Crag)
My two trips up Katahdin was an up and back from Roaring Brook using the Saddle Trail the day before the 7/4 holiday years ago & I was able to show up at 7:30 and get in. (Those days are likely gone) The other was a trip up Helon Taylor, across the KE and then over to Hamlin & down Hamlin Ridge. If you can pick a perfect day, I'd reverse that second trip. Only issue I have with BSP (it's a tin issue) is that all day hikers start about the same time as they enter the pack about the same time. Trails to the top are about the same distance so it can get crowded on the top. (Not Washington crowded) Doing Hamlin first would get you to Baxter Peak after many have left, it may put you in the PM Thunderstorm part of the day though.
Besides the Brother's Loop, OJI. The Owl, South Turner and Double Top are worthwhile too. IMO, in the East, there is BSP and then everything else.