You can get LED tape lights, which work really nicely and require just one transformer at the top of some upper cabinet. Place them about an inch away from your front light rails, so that you don't get a shadow, and you should be set! (I defer to others about brands.)

Bazz Self-Adhesive Cuttable Under Cabinet LED Strip Light, 140" · More Info

I echo what @acm said, and if you want to get fancy, you could get some channels with diffusers to put them in. LEDprofiles.com has a ton of options.

If you are happy with the location, switching, and throw of the current lighting, and those lights are probably direct wire, then it might be a good option to continue with direct wire LED fixtures. Going to tape lighting would require some extra wiring steps, and depending on how your light valance is configured, possibly some other work. You do have a very tall valance, so that needs to be considered with the fixture choice and placement too.

For the hood, it depends on how much space is around the hood "insert." You don't really want to build any sort of valance or reveal to hold a fixture as that would collect grease and spatter. You also probably want to switch the hood light separate from the UCL. So without a picture, I might submit that buying a new insert (or hood) that already has the lights built-in may be a better solution in the end.

@3onthetree Yes, those lights are direct wire, and we are happy with the location and throw. The switching is not in the greatest place but I'm guessing that the cost to change it would be more than I'd like to pay to improve it.

What is the extra wiring that would be required for rope lighting? Something to do with a transformer?

As far as the hood light, I would be OK with it being on the same switch as the UCL lights. The fan has never been a great success - it should have a larger duct but when we renovated the kitchen the installer just put it in without increasing the duct size required. We've talked about fixing it for years but it would probably require more work than we are willing to do.

Going to tape, you'd have to wire a receptacle at each of the 4 existing cables coming out the wall (abandoning a whip may not be possible depending). Then you would plug in the tape transformer at each one, or run the tape across the cabinets and utilize only 1 (or 2 transformers if split). It looks like the sizable valance can hide any receptacle and transformers (they become pretty bulky). If you can't hide them, say with a low nearby seating area, then you'd want to run them into the cabinets above. Then you have to figure out what style of tape channel and placement that will lessen the "hard line" of light on the front of the counter that the deep valance will create. Though if you have a single wall switch for all the UCL already, that is a step ahead - usually the old fluorescents have a toggle switch on each fixture.

My advice for just switching out to LED fixtures, since you are happy with the existing throw of light and where they are, can be a DIY endeavor just like replacing a chandelier. And, you can experiment with different fixtures (there are dozens of tiny differences) easily with DIY where with an electrician you can't really do so easily.

For the hood, a pic looking up underneath would help - you may not have room for a light at hood level, and I would advise against any reveal (like a "shelf") against the backsplash.

@3onthetree Any thoughts on just replacing the bulb in the existing fluorescent fixtures, as discussed on this site that we found? If that doesn't work, agree that switching out for new LED fixtures is the next simplest option, and we'd put the bulb as close as possible to where the fluorescent bulb is now, because the light throw is good.

For the under hood light, my apologies for the messy condition of the hood. Years ago we stuck a battery-powered LED light up there, on a motion sensor. It didn't really throw enough light and it ate batteries like crazy, so at some point we stopped replacing the batteries.

I really appreciate the help with this!

just get LED bulbs for what you already have I would stay around 3k as too white would look odd in your space.

@3onthetree You are correct on all counts.

The smallest T5 fluorescent to the right of the range hood is installed diagonally so it's 12", longer than you'd expect looking at the photo. If we can get replacement LED bulbs in T5's and the right length, we will be tempted to keep the existing fixtures. But given that everything is 27 years old, getting new fixtures may be wiser, especially if we can follow your advice about the range hood.

Because if the existing ballasts start to give out shortly after replacing the bulbs, I would be annoyed. And the "things giving out" thought makes me think seriously about a new range hood fan, maybe with its own light, as the existing fan has been making new noises lately. Nothing lasts forever, although I still think of this as my "new" kitchen.

Could we really be breaking through years of analysis paralysis on this problem LOL??

1000bulbs.com has LED tube replacements of all types and sizes.

@wdccruise sadly it looks like there is no 12" option in T5s, or any other number. And I just looked more carefully at our longer ones and one is a T8, and 2 are 24" T12s. Looks like these types of bulb-only fluorescent-to-LED conversions are more common in commercial applications. Thanks for the link, it's good to know that.

Although I prefer to "reduce, reuse, etc." the odds are not looking good that I'll be able to replace this motley assortment of bulbs with replacement LED's of right size, length and colour temperature. Ballast - bulb compatibility is an issue too.

I think we'll get 4 new wire-in LED fixtures.

Still thinking about the above-stove light. I'd hate to wire in a new light and then have the fan fail. It's giving us fair warning by its new noises.

I don't see a filter - you might just have scrum buildup on the fan blade. Although if uneven weight buildup that could alter the balance of the bearing over time and lead to noise and eventual "kaput."

This style doesn't have a filter but that's a good idea to check.