That is a nice old groove. Reminds of my high school days in Florida.....

The term 'slightly swung' is very accurate. I've really enjoyed Stanton Moore explaining how a 'swung feel' can differ and that there is a 'sweet spot' for grooves that is just as you described it - close to straight but slightly swung. Masters of New Orleans style playing ooze this inbetween-feeling groove and I am always working on it to make it feel better.
Some of the old rock and roll recordings had this approach (unintentionally I believe).
IMHO, FWIW, etc.
Jim