It's possible 18 watts from 396 miles away though the conditions that allow a signal of that strength would need to be nearly perfect with all the other stations on the air at the same time
though I wonder if that 18 watts could even reach the ionosphere and hit it, and bounce back down. I would try again earlier than 8pm and see what the station sounds like and wait for the power to be reduced from 5kW to 18 watts.
I've been fooled before thinking I got a low powered night signal only to find they were on daytime power. Many stations either have not programmed power reduction timing correctly, or are careless. A few might not care, but who wants a fine from the FCC?
I do remember hearing a station from Northern Michigan on 1110, WJML, many years ago and according to the radio listings - 10 watts! 284 miles. But do I know - for sure - that the station was on nighttime power, or daytime of 10 kW?
I believe there is another Relevant Radio outlet in the DC area - WQOF - I was trying to ID it; two Relevant stations mixing together...but I lost it due to pattern change and/or WSDZ Belleville, IL was starting to completely drown out the possible DC station. But it could be what you heard in FL, signal pattern favors your area. WSDZ nighttime pattern seems likely as well into FL.