Is my itinerary for England too packed?

1. 1-1.5 hours for a day trip is fine. And those places sound lovely:)

2. Unfortunately there isn't great public transport through the Cotswolds at all. The simplest way is to change trains in Reading. There's no need to go all the way back to London. I'm not sure of the route from Stratford-upon-Avon.
   It's a shame that public transport isn't better in the Cotswolds because you could consider going to Bath via Lacock and Tetbury. But the Cotswolds are ruled by buses and you'd likely have multiple changes, and deal with bus lines that run once or twice a day. That's certainly an option, though.

3. The London-Canterbury-Rye itinerary would certainly benefit if you want to have more time in those places and not be limited to a day trip. The worst that could happen is you end up in another town and you just get the train back. It's all an adventure.

Otherwise your itinerary looks not too packed but not too boring, a perfect balance. Enjoy your trip :)

I liked Iford Manor gardens but drove there down very narrow country lanes. Sounds like you are not hiring a car. That being so, to reach Iford Manor, you will need to take a stopping train from Bath to Avoncliff and then have a substantial walk to Iford Manor. Click this link for a Google Map of the area and streetview where you will have to walk on street view.

Lacock & Tetbury are OK but I would not rave about them and they are difficult to reach from Bath without a car.

Consider taking a day trip from Bath to Salisbury by train and then the shuttle bus to Stonehenge and be sure to visit Salisbury Cathedral before returning to Bath. Alternatively, take a train the other way to the Cardiff = the Capital City of Wales. Both places are just over 1 hour by direct trains. Cardiff has a castle in the middle of the city - about a 14 minute walk from the Central station.https://www.cardiffcastle.com
You could also visit Cardiff’s waterfront - known as The Bay - 1 mile S of the City Centre - Cardiff Bus 6.
(3 other castles are around Cardiff but you would not have time for these on a day trip).

Day trips to both Canterbury and Rye would work and you have enough time to hit the high spots in both. It also means you don't have to pack up and change accommodation for one night. If spending a night in Canterbury, you would need to take luggage and arrange for it to be stored (hotel) while you explored the town. Would you be going back to Canterbury after Rye, if not, then you will have to take luggage to Rye with you and what arre you going to do with it during the day? Don't make life more complecated than it needs to be!

Rye is a pretty town but give a tight timescale I’d use that day to go somewhere else, like Hampton Court Palace, unless you have a specific reason to go to Rye.

I suspect that it will be just as quick to go back to Oxford at the end of your day tour. It's only 75 minutes by train from Oxford to Bath.

Lacock & Tetbury are OK but I would not rave about them and they are very difficult to reach from Bath without a car.

In the case of Lacock, not that hard. Train to Chippenham then the hourly bus X34 from Chippenham to Lacock (the bus is heading for Frome via Weybridge).

Moreton to Bath isn't 3 hours- often it is change at Didcot Parkway- depending on that connection it is 1:50 to 2:30.

Get the hourly bus from Moreton in Marsh to Cheltenham, taxi or bus from Cheltenham Bus Station to Rail station then just over 1 hour by train to Bath via Bristol.

Iford- frequent train to Bradford on Avon then taxi.

Tetbury is possible train to Stroud, changing at Swindon, then bus #69, or train as above then bus #882. The buses are frequent enough to make a day trip work.

Canterbury has two train stations, so take a look at the map to see whether one will be more convenient for you.

When I daytripped to Canterbury pre-pandemic, the tourist office was offering at least one walking tour of the historic center. I enjoyed the tour I took.