@Bob H. Hey there I’m a contractor up here in Pittsburgh. I deal with this all of time. I would do this.
1. Pull the laminate that is there, you will have tons of movement issues if you leave it. Lay 1/4” utility board in its place to bring up to tile level or just use transitions most lvt manufacturers make one trans that is multi level for step downs.
2. If the grout joints are 1/8” or less just go right over it. If they are larger you will need to skim with a leveler to prevent transposing.
3. Go right over the sheet may need utility board in there as well if it’s not or just use transition.
Note: Transitions come in 7 foot sections if your kitchen entry is smaller than that you could trans there and not need the utility board.
You still may need to cut jams, trim and doors. But I feel that’s easier than tearing everything out and possibly still not have enough room.
Hope this helps! Feel free to reach out if you have any other questions.