Done that, been there
At times, jobs in the IT industry get like that. The load can get quite heavy.
However, I have found that GTD got me through better than anything I tried before. I found out that repetetive requests or uncleared outcomes contributed a lot of the "I am being overwhelmed" feeling.
That is, repetitive requests by clients or my boss which I did not know being repetitive. So if someone asked me to do thing X five times, it would feel like I was being asked to do 5 things. Getting my GTD together helped a lot, it reduced the stress and made me more responsive and prepared. Having the projects and NAs in writing also made it easier to spot unclear outcomes and get those back on track.
You said:
"how do I make more GTD review time for work related material without unpaid overtime"
To which I have to reply that I never had that problem. My GTD is work and life rolled into one. So when the weekly review comes around, everything is being reviewed.
I found out that the weekly review does not get much longer with work - related stuff in the same system, but much longer with 2 seperate systems. This is especially true if you are prone to get work-related ideas outside of work and vice versa.
To collect the next actions or even projects during work, I used a stack of old printouts, folded in half. I'd enter these notes into Outlook (my GTD base) at the weekly or before, if I felt like it and had 5 minutes. If not, I'd scratch out / add to those lists on paper. Yes, that includes outside-work projects as well.
I hope that helps a bit,
::emp::