some photos and dimensions of the whole room and the width and height of the recess will help explain your dilemma but not sure about the glass doors as the shape and size of the glass would be probably be different sizes above and to the side of the fridge and expect that they would need to be expensive custom made doors

Its going to stick out no matter what you do. Is there no budget to reface the cupboard doors and drawers? My Only Suggestion is to not do a White Gloss and instead use a Ravine laminate or a totally different colour and use the colour somewhere else in the kitchen like the off cuts for a frame for some artwork. Or on the kicks. If its going to stick out, and it will, then go all out.

The next best option is go to a joinery company ask if you can take some off cuts out of the bin, make a temporary shelf and save up so you can do everything at the one time. If you redo the kitchen you will end up redoing that cabinet to get a consistent colour. Even with colour matching there is still slight differences because one is new and the other is old.