Can't see the photograph.
You may need to cut away more of the back than you suspect - your upstand is 20mm thick, but the service void is 17mm and the back is 8mm thick (so 25mm). Standard batten is ex-2 x 1in softwood (so 44 x 22mm from many merchants). I'm concerned at how you think you are going to cut out such a large chunk of the bottom of the cabinet and then replace it by such a thin piece of MFC(?). Your sequencing is all wrong - you need to put the strengthening in firstt, I think it will need to be more than 30mm(?) and the bottom shouldn't be cut out before the new front stretcher is fixed in. TBH with a need to accommodate hinge cut-outs and a front cut-out I think you are looking at 125 to 150mm tall for it to be strong enough. I am also left wondereing how you will get that extractor in there, as the cabinet plus doors is 320mm deep, but you lose 20mm for battens (leaving 300mm to the face of the doors) whilst the manufacturers instructions calls for a service depth of 307mm (which will leave your extractor sticking out 7mm at the front) - see below:
View attachment 268138
Seems to me that having a 20mm thick splashback without taking the extractor into account is a bit of a design error on the grounds that you are trying to fit a quart into a pint pot so to speak. Maybe you need to consider making up timber grounds to pull all the tap cabinets forward by 20mm or so to overcome this issue
BTW, my original drawings weren't intended to be a worked through design, just an idea which shows how such installations are approached. For a fully worked example I charge!
307mm is the depth of the section of the extractor that sits below the unit (where the filters are), the section that goes inside is only 273mm
The bottom is not meant to be flush with the unit