For what it's worth, my $.02:
Since you already have 2,000 jet it won't hurt you to become a sim instructor, your flight time looks good. In fact, it may help to differentiate you from the rest of the herd by acquiring some training experience. The problem I have seen with most sim instructors is they never return to flying the line on a full-time basis. From an academic perspective, sim instructors are ususally going to be way ahead of the curve in relation to line guys and gals when it comes to aviation "knowledge" simply becuase they are teaching the profiles and procedures on a daily basis. But over time their flying skills can deteroriate... rapidly. IMO, after a year of sim training you really start to loose out of other attributes of flying the line like actual experience, which gives you the database with which to reference for judgement. In effect, you get really rusty after not having touched the yoke for a year.
I was a checkairman/ instructor for many years. I worked hard to continue to fly the line on my days off and eventually moved on to a major. I do not believe I got hired at a major because of my checkairman status. Rather, I believe my checkairman status was a complement to my overall resume. At the end of the day I was measured based on my flying expereince, which included international. While I taught, I regularly did "instructor demos" which benefitted my students and kept my skills in check. Then I would fly on my days off to keep up with what the line guys were doing. It all added up to a lot of work.
Many of by checkairman compadres rested on the laurels of their position/ status. They liked their time off (who can blame them for that), they liked being home every night and just never really got up off their proverbial arse to get out and fly the line. Time flys quickly and after 5-6 years of teaching in the box and only flying "occasionally". Eventually, they were no longer competitive. Whilst their line buddies had amassed 5-6,000 hours more flight time, they had mayber 150 to 200 more hours. Lack of recency of experience shows SWA and any other airline that perhaps you don't like line flying afterall. I'm not saying they won't hire you, but after a year in the sim you will need to keep flying the line 20-40 hours per month or risk stagnation in your experience qualification.
I have two chekcairman buddies who were hired at SWA. The first guy quit the training dept after a year, went back to the line and got hired by SWA rather quickly. The second guy kept applying, and applying, and applying. Only when he started to fly on his days off, and ramp up his recency, did finally SWA call him. And when they did call he got chastized pretty hard for not flying the line much over the previous 5 years. In fact, he was surprised he got hired after such an ass-chewing by one of the captains on the interview board. In short, they made it very clear to him that he barely made it in... barely becuase he hadn't flown much int he prev 5 years. His total time? 10,000 hours including 2,000 in the 737. But only 400 hours over 5-6 years previously.
So I'd say take the job but fly on your days off if you can and definately get back to the line after a year... too many guys stay in 'cause the trng dept because they get use to the $$$ and being home every night.