had I only had a carry-on I might have been tempted to try the train.

To get to Silom you'd have to take SARL from the airport to Phaya Thai, then the Skytrain (Sukhumvit Line in-bound towards Bearing/Samrong) to Siam, then change to another Skytrain line (Silom Line outbound towards Bang Wa). I guess Surasak is the closest BTS station to the Holiday Inn/Silom, so you've still got a pretty long schlep (close to 1 Km) on uneven footpaths.

While there are escalators (up mostly, stairs down), and elevators (newer, hard to locate sometimes), you'll be doing some heavy lifting. Add to that very crowded trains, and queuing for change and tickets (2x) and generally navigating, a taxi might be the better option (260 on the meter, 50 surcharge, ~100 tolls, so ~ 400 all in)?