Larry
It seems your first thought was that your posture didnt look good (as opposed to I must change my posture because I am having pains / difficulties )
Your look may bother you, but does it bother the punters ? I would have thought how the band sounds is number one, or (and / or) how the bands "show" looks if the band has a routine as part of the "show"..... in which case I would have thought feedback from bandmembers would have come your way.
For mine the more critical aspect is how your posture affects your health. I would guess if you videod yourself on the computer, watching TV or eating dinner at the table you may notice a similar "slumping" posture (Its certainly common for people using computer key boards etc)
Generally speaking poor posture sitting can also influence how one stands, walks etc.
This is because your "core strength muscles" are relatively week and do not support your skeletal structure / joints in the right alignement.
Essentially 3 things would need to happen
1/ You need to develop an awareness of how you are standing / sitting and correct this posture if its "out'. That takes some time to develop the awareness, it takes time and practice and will not happen overnight...so its important to be patient. I would also suggest it will be easier to develop that awareness while in a relaxed state (sitting at the table, computer etc). I very much doubt that drumming at a Gig is the place to start....too hard when you have a show to do......but its something you can work towards. It will be much easier once you have developed an awareness through practice in less "pressured" aspects of your life.
2/ How the "furniture" is set up has an impact on how we sit / stand. No 2 bodies are the same...our height in general, how long our arms / torso / legs are in general and in relation to each other ( for instance I have a longer torso and shorter legs relative to people of my height)... So I have problems getting things set up so my legs are able to reach the pedals and tom height / cymbal placement needs to suit my reach)... as it turns out I just cant play anything but heel down.....lifting my knees pushes my torso further back and disrupts my tom / cymbal reach and technigue...)
Most "offices" will het in an occupational health person to look at peoples seating posture at their desks and will reccomend specific thngs like seat choice / height and squab settings and a range of other matters.
3/ To develp your support muscles you can get a set of exercises for the home, gym or pool that will stretch and strengthen your postural muscles which in turn will gently shift your spine into the bodies "natural" posture.
This in turn will make it easier to "hold" your new posture and make it easier to "find" the correct posture during your awareness / correction activities mentioned in part 1.
I say these things confidently as I spent years in the vocational rehabilitation industry dealing with (amongst other things) postural issues, especially for people with musco-skeletal problems.
I would therefore with respect probably not take postural advice from this forum (unless the poster has specific training in such matters)
Rather I would take your drumming video, along with videos of you sitting at dinner, the desk etc to a physiotherapist or an occupational therapist.
See if they have any concerns relating to posture and if so get some exercises to do, get advice on developing postural awareness and maybee even work out a cheap way of doing an assessment of your "work station" AKA your kit.
You should be able to claim such advice as a tax exemption (you can in Australia).
NOTE I said physio or Occupaional Therapist NOT CHIROPRACTOR
There is bugger all use in cracking your spine in place if the structural muscles are not able to hold things in place. Your bodgy muscles will just "pull" the spine back to where it was.
I am not bagging Chiros..they are good for certain conditions, but postural change is long term and reqires muscular and workplace change to be effective.
Hope that helps
all the best
Wombat