Shower/Tub backer Board

Hello I would appreciate some advice with a problem. First let me set the stage by letting you know I'm selling this 20 year old house in about 1year (no more than 18 months). Time and money are in very short supply for this project.I am very comfortable taking on the tiling, even though I haven't done this as of yet.
I was regrouting my shower/tub in the master bath (which is along an outer wall) and found the bottom 3 rows of tiles along the length of the tub were loose. Of course as you figured, water damage to the backer board. There is serious rotting damage to the lower portion (about 1.5 ft) of the backer board, however it didn't seep through to the drywall or studs. It appears that there is a wood frame (2x4?) around the upper edge of the tub that is attached to the drywall and that either supported the backer board or is just framing. In any case, its not damaged either. The upper portion (2.5-3ft) is damp, but the tiles are sticking very well.
Here are my initial thoughts that I would like opinions on:
While not ideal, and if I were staying I wouldn't even do this, but replacing the bottom portion with new backer board of the same width, using rust proof/special screws, filling the seams to seal (not sure with what, suggestions?) and reusing the same tiles and regrouting.
If I remove the entire 6x4 area (the length of the tub), then I also have to remove the other 2 sides as well to properly fit this part in, since it appears that the builder put the long backer board in then the sides. I'm trying to avoid this at all costs.
Please feel free to email me your suggestions
Thanks Ben

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