subwoofer 19 by 18 room

I cannot agree more with Bob Reynolds on setting up the sub.

Apart from that, bass traps behind the speakers at the corners would substantially improve bass definition. I have read from a few posts that they don't help in some rooms but once I took out the bass traps from the corners of my room, the definition was lost and bass got considerably loose. That was the point when I figured out I cannot live without those traps.

Yes! What Bob Reynolds is infering here is correct! You simply don't know what all the variables you were dealing with
are, and their impact (no pun). Single 3 biggest issues for sub performance is location, location, location--then setup, level matching, phase with speakers/seating, and EQ'ing!!!
In your still relatively smallish room, I suggest passing on the Arcam (which lacks severely needed EQ and DSP room correction features! Any relative potential great sound quality will be mostly voided by the likely bombastic room mode problems you'll likely have, as well as other acoustic issues. That's my perspective. Infact, in all these smaller acoustic spaces, that's one of my main issues! That being that even the best potential audio equipment is necessitated by needing EFFECTIVE room correction or EQ'ing! Most high end gear doesn't include much here(yet). I'd like to see more, because it's a HUGE ISSUE! Food for thought here.
Yes, the Arcam is an otherwise good sounding piece, on it's own. But then what about the extremely difficult acoustic issues you'll be faced with? That's the dilema, IMO.
As for Subwoofers, and your original post, if you have to go with one sub (not knowing sub placement and setup), I might suggest you won't go wrong with the Paradigm Servo 15--especially for the money!! You'll spend more on a sub, and not get more really. Overall impact, extension, lack of distortion, tightness, relative accuracy, quality, etc.
That's my blind suggestion.(unless you don't end up with a system EQ, then look into others like Velodyne, with Parametric EQ feature) And I've sold/used a lot of subs over the years, and don't think you'll beat this, overall.

one can always tact if the room doesn't work

honestly the singal from my two front channels will mostly be absorbed by the couch

open ended on three corners I doubt the room modes will be that severe
(other than maybe the low one that the JL Audio sub can kill)

"honestly the signal from my two front channels will mostly be absorbed by the couch"

No this won't compute much here. Bass modes will still abound, even with the largest of couch and furniture infront of the speakers, regardless of what speakers the bass is coming from. The room modes will still excite, and be audible.

"open ended on three corners I doubt the room modes will be that severe"

Doubt? Yeah, if you get in there an measure (and listen) through the frequency sweeps, you'll be able to tell where you're at--which is the only way to tell. Yes, possibly, depending on seating arangmenents, you may or may not be able to get away with good fidelity and smooth response, in some possitions. But you gotta measure and test to find out, yes.
I've not seen the room, but Know from experience what usually ends up is modal problems at certain points, regardless of how open the room is. I hope it works out very well for you however.
I recently did a lawyers home theater in the main living room, that was open on both sides of the listening space, and the room was 21feet deep x over 33 feet wide (43 in once spot)to the open spaces, with a 10-11 foot tiered/coffered ceiling. After running through all the test frequencies, and test material, the owner strongly concured that we needed another pre/pro in his system--one that had a parametric EQ built in, at the time. Problems solved, the 3 main bass mode problems were eliminated (over 20db boost at two frequencies!!!!!...bombastic to say the least!!!!...not hi-fidelity).
Anyway, it's always a consideration. Nonetheless, I do hope you get better results with your Arcam option, if you go that route