Need to expand microwave box on IP 350. Any cabinet maker tips?

I have an IP 350.  The existing microwave box is 9.75" high, 19" wide and 11.75" deep ( I could stick out to 12.75" deep)

Based on my research I could not find and microwave that was under 9.75" high.  It appears that I will need to remove the shelf above the existing microwave.  I was able to find microwaves around 10.5" high.

There is a bottom board that I could remove, but  think it is there to help water spilling over from the sink from going under the microwave.  So I really do not want to remove it.

Does anyone have any tips on how to do the cabinetry so it will look nice.  For example use a hammer and board to knock off the shelf molding and cut it down.  I am assuming that the joints are all glued?

Has anyone rebuilt the cabinets above the counter tops?  I was thinking of doing this to make a more efficient design.
 

I would be surprised if that top piece of molding isn't glued as well, but your first step should be removing the bungs and the screws which will then be revealed.  A pull saw will allow a thin, smooth cut to remove just the portion above the microwave.

Thanks for the tips. I found one microwave that may fit and ordered it yesterday. If the measurements are correct, it should work. The one I found was Mainstays 0.7 Cu ft Countertop Microwave Oven - Color: White MSF0B100072352 (L x W x H) 17.60 x 12.70 x 9.60 Inches. I will let you know if it fits.