The range top would go in the general vicinity of the proposed sink. You can play with your drawer base widths to make sure that you have adequate space on either side of the range for prep and a landing area. When cooking, we want to go to the fridge for produce/proteins, the sink to wash anything that needs it, then prep between the sink and range. It's nicer for the cook to have an efficient path when preparing meals. Whether you move in straight line down the countertop or have a triangle, ICE-WATER-STONE-FIRE is a GW goal in kitchen design. If you can achieve it, the kitchen is working FOR you instead of you working around the kitchen's flow limitations ;) TKOs don't like barriers to work flow traffic or backtracking. Your compromise is that the range top isn't in the center as a focal point, which I believe is the purpose of it's placement. My new kitchen has the work area along one wall, similar to yours. It's not as step saving as a triangle can be but, like you, I have limited wall space. Fridge is on a short wall perpendicular to the pantry/work path. I have pantry, counter, sink, counter, cooktop, counter, wall ovens. The wall opposite is where dishwashers, cleanup sink, and silverware/dish storage will be. If running plumbing to the island for a prep sink isn't possible, I'd like fridge, counter with dishwasher underneath, sink, counter, cooktop, counter. You're going in one direction and the d/w isn't in the prep area. If you have a sink in the island, keeping the range top in the center makes sense for work flow.

Now having done both and seeing the drastic difference in results, I would never pay a painter to paint cabinets with standard paint products. A lot of the cost is the prep work (labor is high these days). Standard paints can never produce a professional result and will not have the longevity of lacquer. I would go with a true pro and have them use lacquer paints. You will be much happier in the end.

I was trying to address the big issue that I think, if it were my kitchen, would bother me the most...deliberately mismatched cabinets or trying to make them match and failing. It's doubtful you will be able to get a perfect, or even a great, match by painting the new cabinets to try to match the new ones. I know it would bother me to have a different color on connected cabinets. I'd rather pay a bit more money to reface the existing, if Diamond offers it, and get new doors to match. Have you priced out what it would cost to replace them all? You could modify the layout a bit to add more space b/w the range and sink (the most important workspace). Maybe you could even move a couple of cabinets around to gain space. Move the "old" 36" to the other side of the range and get a 42" one (or 18" trash pullout + 24" drawer base) for b/w the range and sink. But then, you'd need new counters all around. Even on a slab, you can often move gas or water a bit in either direction, so you might be able to gain 6 to 12 inches b/w the range and sink. Sorry, there I go blowing up your budget again! I just know that over time I would be kicking myself for not doing more to match the cabinets and, possibly, to add workspace where it's needed most. If just adding the peninsula: Don't get a blind corner cabinet. They're poor cabinets. Instead, get a 27" and turn it 90 degrees or void it out completely.

When I did my kitchen, I used a broadly acceptable finish for my cabinets and used my very taste-specific color preference (chartreuse) on the walls. When I eventually sell (or rent out), I can repaint the walls some inoffensive and broadly popular color and no one will ever know how delightfully cheery my kitchen was. I'm not saying you shouldn't do green cabinets, just pointing out another option.