A fault affecting one colour is most unlikely to be a bad capacitor. The possibility of a bad tube is fairly high as you've just described the classic symptoms of the heater-cathode insulation on the red gun failing leaky. If it had actually failed shorted, it would probably have tripped the excess beam current protection circuit.
Try isolating the red gun cathode at the CRT socket by desoldering the pin. If the excess red (and the red in the picture) all goes away leaving you with a G+B picture, the fault's probably the drive circuit, which can be confirmed by isolating the blue cathode and patch wiring the red drive to the blue cathode - if the fault moves to blue you then know the CRT is OK. If with the red cathode isolated, the red is still flooding the screen, that's confirmation te tube is bad. That normally means its B.E.R. but if a customer was particularly attached to their CRT TV and couldn't afford a new tube, we used to fiddle around with an isolated heater supply which would let the heater follow the leaky cathode, so it did't increase the beam current, at the expense of poorer horizontal resolution due to the increased capacitive load.
If its *NOT* the tube, try to find a copy of the service manual online, you *WILL* need it.
Betting on getting it going well enough to trust for a wedding in three weeks is *NOT* a good idea. Start by asking the venue if they have video projection facilities - it will be a lot easier to run a slideshow on their kit using your own laptop or DVD player, but for ****'s sake *TEST* it ASAP, with the actual laptop or DVD player you are going to use, and if you stick with a slideshow on DVD, with the actual slideshow DVD. Not all DVD playes are equal and if the slideshow hasn't been properly rendered to video a name-brand player may well not play something a particular off-brand player is fine with.