I'll defer to the experts on GW about modifying the cabinets, but don't overlook the importance of hardware. I think slab doors have the advantage of being anything you want them to be -- if you build a more traditional kitchen around them with hardware and light fixtures, they might not even register as modern. I grew up in a house with slab front cabinets, and there's no way you would have thought that kitchen was modern.

before altering them I would work with counter edge profile and backsplash to move the look to more transitional....as well, is there a window or two you can do a change-up visually?Window treatments such as fabric valance/rod/rings/etc. can change the feel of the space. Faucet style can also add to the "shift' you are trying.

I think it can look something like urban/country or European streamlined country. The kitchen below is contemporary but with different backsplash, light fixtures, chairs could look more traditional. I love the look and wouldn't try to make shaker doors out of them.

[Modern Kitchen[(https://www.houzz.com/photos/modern-kitchen-ideas-phbr1-bp~t_709~s_2105) by Austin Kitchen And Bath UB Kitchens

Maybe some glass inserts and shelves:
{{!gwi}}
{{!gwi}}

And below, a link to pretty much the same kind of discussion thread.

Here is a link that might be useful: slab doors and transitional/traditional

herbflavor-
what can you tell me about modifying the edge profile of the counter? I've considered this and think it might be doable with the corian.

Ditto herbflavor! Hardware, backsplash, window treatment, and faucets can make a huge difference! I wouldn't worry too much about the slab doors' "modernity".

corian has edge offerings. several of the ogee or french cove have more traditional flavor if this is really the way you want to go. there is a lot to be said for an eased edge but take a look at the options if you are certain of your goal. Houzz searching of "corian counters" might show something clever beyond the typical eased edge. another "traditional" thing/or warm cottagey feel might be had by inserting wood counter somewhere. Breaking up long runs of the same counter material gives the eye places to land and if you're worried about the effect of all the smooth doors,adding another texture or element can do things.

As herbflavor said, your house sounds like transitional style. You can certainly use slab doors to get a transitional kitchen. I think if you stayed away from crisp, contemporary straight lines in the faucet and hardware, going more for gentle curves, you could get the feeling you want without changing the doors.