Yikes - yes keep the head on the cap with solution if you are going to stop working on the problem for more than an hour or two.
JV33 head swap is terribly simple. I replaced ours a week or so ago. Literally printing again in under an hour.
Needs-
New Printhead (preferrably with correct manifold)
Big syringe with a DX4 head style damper
Bottle of cleaning/flush solution
First remove the carriage cover, then both damper retainers. Unclip head cable holders. Pull head temp/memory thingy off the front of the manifold. Remove both head hight adjuster posts. Pull all 8 dampers off the head mainfold and to the left side. Be VERY careful with the dampers - DX5 dampers have VERY sensitive compression valves on the sides - the lightest press on the side of a damper will open it causing ink to flow out fast. Remove both thumbturn head retainers and the plastic washers under them. Pull head plate with the head loose and pull the 2 ribbon cables off the head.
Prep the new head - SLOWLY over about 20 to 30 seconds per channel inject about 20 to 30cc flush into each channel of the new head using the syringe and DX4 style damper on each damper post of the new head manifold. Once done remove the 2 screws attaching the old head to the head plate, cleanup the plate also noting which way the flat spring thing goes on the one side and attach the new head to the plate.
Being VERY careful and mindful of the bottom of the new head attach both ribbon cables to the new head. Clip the new head plate and head into the carriage. Install the thumbturn head retainers - these need to be just right so that when folded down they are snug - one turn too far and they will be super tight - one turn less and they will be loose.
Put all the dampers back on and their 2 retainers. Reinstall height adjuster posts. Resecure head cables, reattach head temp/memory sensor thing to the manifold.
Power up - enter service mode and enter the new head rank (if available and/or valid). Do an ink fill up. Run a Dot Position Correction. Print away!
Optional steps. Might have to re-use your old manifold depending on if your new head came with a solvent manifold. The other thing to be aware of - many non-mimaki head have a solvent manifold that is not 100% compatable. It WILL work but your head temp/memory sensor thing will not attach to the manifold correctly. I simply removed mine from the plastic peice that holds it and stuck it to the new manifold with a small bit of banner tape and it works perfectly fine.
Finally - installing a head the way I described it here - I only did one single ink fill after the install and was getting 100% perfect test draws. If you are still having problems I'd consider replacing the dampers and capping station top. Be aware - on a JV33 - the ink system is CLOSED with valves behind the cartridges. If you use a syringe to draw ink into the dampers or the head from below the capping station without opening the ink valves first you will be creating a tremendous amount of negative pressure in the ink system potentially damaging the dampers.
Anyways - it's really hard to tell what is wrong. I'd start with the dampers and capping top myself though.