Transit time in Haneda

I will be flying from Seoul to Haneda in April. Have already booked travel from Haneda back to the US.
Trying to decide how much time to allow to clear customs and immigration for the flight from Seoul. Only carry on luggage so no need to collect bags.
Thanks

I'm not sure, if you have to go through immigration and security checks if transferring from Korea to the US at Haneda, but you seem quite confident with that, so I'll go with it.

Given that your inbound flight is on time and you'll be checked in to the outbound flight, in my oppinion, three hours is an absolute minimum, but I'd opt for a safe four or five.
If everything goes smoothly, it can be done quicker, but I would not count on that, as immigration and safety checks can be very quick or take quite some time, even if the average time is a lot shorter than in Europe or the US in my experience. We recently waited very long at security in Haneda. And there was no priority lane, in case you can use that.

(In case of transfer without safety check and/or immigraton, this can be shortened to maybe two hours or less, so maybe someone can comment on that?)

BUT it sounds as if you'll be booking the flights seperately, so you won't have a guaranteed connection in case of delay or cancellation.
Depending on your booking class for the 2nd flight (rebooking or cancellation possible?) I would allow a MUCH longer transfer time.

(Personally, if cancellation or changes were not allowed, I would fly to Haneda one or even two days early - but that might just be me being extra careful.)

We don�ft really have the option of flying into Haneda a day early unless we leave our tour early. May just opt for a flight that leaves 3 hours earlier which should give us enough time (almost 6 hours)

Appreciate any other thoughts
Thanks for your input.