If you want to keep a broad swath of light you could use a long rectangular flush fixture. There are also square flush fixtures. Also consider an upward shining floor lamp to brighten dark corners.

can you put in canned lights? that would be the best option.

or, try some of these

not quite sure of the name for this (other than 'up-lighting') but you could run a type of molding or frame around the perimeter of the ceiling, and install the rope lights that would also run the perimeter. kind of like a tray ceiling, but not really.

Thanks for the suggestions. We’re trying to avoid the cost of canned lights. although I agree they would probably look great. I like the flush fixtures as well, especially the round ones, as long as you don’t think they would look odd next to the existing large square recessed lights! My husband wants to put new track lights in, something more updated looking. Is it possible for track lights to look good over a fireplace?

LED flush mount fixtures come in both square and round formats. One possibility that only occupies 1-1/2" of vertical space is: https://lithonia.acuitybrands.com/products/detail/579430/lithonia-lighting/wf6-downlight/wafert-led-indoor-outdoor-6-in-housing-free-recessed-downlight

If it were me, while I was at it I'd remove your existing fixtures and update them to LED as well.

Track lights over fireplace:

https://www.google.com/search?rlz=1C1GCEV_enUS875US875&q=pictures+of+track+lights+over+fireplace&tbm=isch&source=univ&sa=X&ved=2ahUKEwi3pIrv5Z7nAhVhS98KHf0nA6QQsAR6BAgIEAE&biw=1280&bih=610

Lets back track, what is the budget you have to replace these two lights? you would spend 200$ just updating the track. are you planning to scrape the ceiling?

Canned lights are cheap! They're $11 at the home center (for retro-fit/old construction). Just how cheap can you expect?

Skip the can lights, LED flush mount fixtures can be had for ~$25 +/-.

It’s the cost of hiring an electrician to rewire the ceiling in order to install canned lights that we’re thinking about. Re: scraping the ceiling, all of the ceilings in the house are popcorn(!) so we’ve decided to just embrace it. I would prefer to put the money into attractive lighting that doesn’t require retiring, unless everyone thinks it won’t look good unless we put in canned lights. Budget is up to $250 per light. I had a higher budget when we renovated our main floor but I’m trying to pace myself because we don’t use the basement as much. Thanks again for the ideas!

Beth H. I was inspired by your suggestions! Anyone like any of these for the spot by the fireplace?

How tall are your family and friends? If your sons are 6'6", then they're likely to hit their heads on those. That extra clearance is what makes the cans desirable.

We’re all 5’6” or shorter! I know what you mean though, don’t want visitors hitting their heads either...

I would start by retrofitting the existing square can with an LED kit that screws into the exsisting socket and that will help those produce more light than they are now. something like this:

https://elcolighting.com/products/8-square-led-retrofit-insert

In front of the fireplace, you could keep the existing track there and just get 2 smaller track heads

for the one by the tv. its just in a very redundant spot. After you brighten up the existing cans see if you actually need that light. if you do I would put in a 4 inch recessed light with a square trim. or a single spotlight aimed at the doorways.

i like the first 3. you can always use LED bulbs in place of a bulb that says 40W max on there. LED comp bulb is like 6W for 40. so do a 75W LED bulb and get more light output.

the lights w/milky glass will diffuse your light. so just depends how much light you need for those fixtures.

I think open light bulbs or light bulbs that hug the ceiling will only bring more shadows to the popcorn ceiling. directed light or down light would be better.

if you want flush square lights you can get them pretty easily... these are available on Amazon however I know Cooper lighting / Halo made some square ones too that our electrician was able to order. These are super easy to retrofit into a drywall ceiling.

It's going to cost just as much to install the flush-mount lights. The cost comes from running the wiring, and both types of lights need exactly the same wiring. Why do you think it would cost less?

And those surface mount lights give off ghastly, ugly light (and may not be dimmable)..

not true you get the right color temp and they are fine. The wiring is already there for the track, they are talking about running additional wiring. I was talking about just exchanging the existing squares to LED and then adding more light as needed.

You could run the pot lights off that one circuit and honestly they are pretty cheap and not a lot for an electrician to do. This room was in a basement with the same ceiling height as you have and we put eye

ball pots to light up the space more than the ceiling. BTW no windows in the space .