Don’t worry – if you do a good job sealing the remaining 1″ of fabric to the floor it will be more than strong enough. I design the overlaps to be much wider than necessary for a strong bond, and even half the width there is more than strong enough, assuming proper heat sealing technique over the entire weld. Sealing the cut-off piece of fabric to the floor wouldn’t help because it’s not connected to anything – the only reason I can think of why it might make sense to do that is if your iron is wider than the remaining part that will be sealed to the floor (to avoid ironing TPU directly), but because you trimmed it, I assume that isn’t the case.
If a reinforcing strip will give you peace of mind, you can add one to the outside of the packraft covering where the floor meets the tube. In most packraft models that would be on the bottom of the packraft and not noticeable, but on one where the floor wraps up above the waterline (e.g. Telkwa) that would be visible, so I would probably use black fabric and reinforce all the way around the packraft to make it look like it’s supposed to be that way. But again, it’s not really necessary for strength.