Make sure you go to those rides first (you probably would anyways!) As they walk throughout the day, theoretically their spine shrinks some, plus their shoes get worn down some, and they get tired and slouch more. I'd also recommend making sure you have a good pair of shoes. Not high heels, but tennis shoes can vary between giving the kids 1/4 to 3/4 or so of an inch and all look like regular tennis shoes. Maybe even buy a new pair (I've found the character ones from somewhere like Target tend to have a more built up heel) so they're less worn down.
We went to DL/DCA when youngest DS was like your son - exactly 52 inches with shoes on (there were several 52 inch rides there). I didn't think he'd make it so we tried at Knott's Berry Farm first on the Xcelerator. They measured him and let him on with no problem.
When we got to DCA, at that time they had a measuring station where they used laser lights to measure and give them a wristband. He got the 52 inch wristband and we headed to Maliboomer (kind of like Dr. Doom at US). He rode it easily, both that day and on several other days (we spent 5 days at the parks). On the last day, we headed there (hadn't gotten the wristband in a couple days because we "knew" he was big enough) and they insisted he was too short. We realized that his other shoes had gotten soaked and we'd switched shoes and these were just a bit smaller. No big deal - he'd ridden it several times. Went back to the hotel in the afternoon and switched shoes. Went back there and AGAIN they insisted he was too short. Don't know if he was shrinking by the end of the day or what, but he didn't meet the line.
So I'd recommend trying both rides, even it he misses it at the first. I'd prepare him that if he makes one, he may not make the other, or may not make the first one a second time. Teach him to take a big breath and stand tall and try hard to "be tall". Enforce that he NOT stand on tiptoes because once ride operators see that, they'll be over-vigilant because they think he's trying to sneak on.
As far as you being scared of him going on, I know the feeling. Shortly after that visit, we went to Cedar Point (Ohio) for the grand opening of Top Thrill Dragster. If you're not familiar with this ride, it goes 120mph, pretty much straight up, then spirals straight down. It also had a 52 inch height requirement, which by then (3 months later), he made easily. We stood in line 3 HOURS for the front row, and when he got in, they insisted that although he was "tall" enough, he wasn't, um, "hefty" enough. Apparently the lap bar had to come down to a certain point and his bar didn't come down far enough so he couldn't ride. Devastating, but better than falling out I suppose! We went back a couple weeks later and tried again (this time using parent swap so he didn't wait as long) and they insisted he was fine. I mean I POINTEDLY asked to make sure he was okay, and they said yes. Well, I spent the entire ride gripping his arm (yeah, I'm sure that would have helped if he fell out!) and really was terrified every time he rode it that year. I do know on all the height restriction threads, lots of people have insisted the actual requirements are probably like 6 inches lower to adjust for different body types, slouching, people "padding" their kid's height, etc. So, since your son is actually really 54 inches, I'm sure you have nothing to worry about, but I certainly understand! Good luck!