What exists currently is a fire hazard and needs to be changed regardless of anything else that you do. You cannot have wood directly above a cooking zone unless it's at least 30" above it.

Overhead venting is always superior to downdraft. Especially if you want to convert to gas. A strong wind right at a gas flame tends to do funny things to it. Like suck it out. Overhead venting captures naturally rising steam, grease, smoke, and odors, and if you can have the correct ductwork added, gets all of those nasty things outside of your home. Because all of that stuff rises upwards and outwards, vent hoods always work better if they are at least 6" larger than the cooktop that they are covering below, If you move to a 36" cooktop, you would ideally have a 42" vent above it. And at least 27" deep.

For your wall oven, if you want to replace it, your cabinet needs to be the right size to accept a modern oven size. That standard has become 30" ovens, which usually take at least a 31" cabinet in custom cabinets, and a 33" cabinet in standard dimensioned cabinets. It looks like a 24" oven in maybe a 25" cabinet?

You also need to check the spot where the fridge is, and measure it. It too may not be a standard size to work with today's appliance sizes. A regular free standing refrigerator needs 36" of width and 70"-72" of height.

I'm also not seeing any drawer stacks in the picture that you posted. Many older cabinets didn't see the usefulness of drawers, so all you got was a single one on top of doors rather than a whole stack of drawers. Are there any roll outs below, or is there just a half shelf? Site built continuous cabinets with no internal divisions?

If everything works currently, other than taking down that shelf immediately above the cooktop, I think I would just live with it for as long as it took to accumulate the funding to address the rest of the 30 year old issues that the kitchen has, not just the appliances. One other approach that you may not have considered if you decide to keep the cabinets and just retrofit them is a 48" actual range where the cooktop is, with an actual hood above. That will give you two ovens. Where the oven is located now could be retrofitted by a good cabinet maker to accept a MW on a shelf so that one could get off of the counter. Maybe you could do something like a cutting board/baking sheet rack similar to a plate rack with the leftover space from the oven cabinet.

Just FYI, 24 inch double ovens do exist. Aj Madison is an easy to search website if you are looking for less common appliance sizes. Not saying the bigger size wouldn't be better but if you are sure you just want to swap appliances, it is possible to find 24 inch, as well as other widths for double ovens.

I would try to get overhead ventilation if possible. I don't know how hard it would be to run duct for that--is the cooktop on an outside wall or directly below attic space?

I would consider an induction cooktop. I don't know about sizes on that, but I love love love my induction range and will be keeping it in my planned kitchen remodel.

Here is a link that might be useful: Aj Madison 24 inch double ovens

Thanks for the input. My double oven is 24" and I have done some research and found there are a couple of options to replace it without making too many modifications (except for the height, the newer ones are much shorter). There are internal divisions between the cabinets and there are some drawers on the other side of the kitchen. We actually have plenty of cabinet space, it's a pretty large galley kitchen and the owners really maximized the space with the 42" cabinets. I really don't think I want to wait to redesign the kitchen because the cabinets are really quality cabinets so we want to just replace the older appliances and install granite and backsplash. I do like the idea about putting in a freestanding range instead. It would probably save us a bit (which we'd probably end up spending to retrofit the double wall oven cabinet). I have some unused space in the kitchen where we could actually reuse the 48" base and wall cabinet so we don't lose the storage space at least. I would definitely like to get the microwave off the counter too!