It's fine to glottal-stop the t in 'gently'. A lot of native speakers, though not all, would do this. Regarding the other t's: the t in 'boat' can also be skipped, if you like, because it merges nicely into 'gently'; but it's better to pronounce the t in 'but'.
I've attached a recording of me singing the verse twice! First time with a t in 'gently', second time without. ;)