Is this your PhD you are working on ? While it feels like I am doing your homework I cannot resist chiming in.
I worry that if you have oxygen contamination of the mixture which causes the palladium chemistry to be terminated then the chemical reaction which terminates the palladium could then form some organic product other than the one you want.
You need to consider which point in the catalytic cycle the palladium is most susceptible to poisoning with oxygen. I think that the Pd(0) complex which is a POSH version of [Pd(PPh3)4] will be the resting state of the catalyst, if this decomposes either to a palladium mirror or to a palladium(II) complex like [PdBr2(PPh3)2] then this will just result in loss of activity of the catalyst. If the oxygen does something at a different stage in the cycle it could be worse, then the oxygen could cause the formation of a different product.
I know from Monsanto acetic acid process chemistry that the RDS for that reaction is the reaction of methyl iodide with the Rh(I) complex, while with BP’s Ir based process the oxidative addition is not the RDS. There the more heavy Ir as it has a stronger C-M bond has different chemistry. I worry that a Pt catalyst would be a lot more expensive and it would also be more sluggish.
I suspect that adding more of the palladium catalyst will not do any harm as the poisoning of the system by oxygen or the formation of the palladium mirror which I used to have sometimes on glass flasks will not do too much harm.
I note that the colour is similar to many palladium compounds, I would be inclined to use thiol-SAMMS (a mesoporous silica with a monolayer of mercapto propyl groups) to remove the palladium which is still in solution from the solution of the polymer.
I think that you need to rethink the polymerisation reaction, I would want to keep the polymer in solution as long as possible during the polymerisation to stop it coming out of solution before it has fully grown. I would want to try to do the polymerisation in pure DMF in the sincere hope that the product would be more soluble in the DMF.
I would suggest that you take great care with DMF, I hate the stuff. It is viscous and toxic. I say it is an equal opportunities monster. I know that it is linked to testicular cancer in men and I am sure it does horrible things to women. I know it is a teratogen so keep away from it if you are pregnant. Some chemical companies will not allow any women to work with it. This is not a totally unreasonable thing, I know that some nuclear companies keep women under an even stricter set of rules for radiation than they do for XY chromosome owners like me.
I think that you should try to get a nitrogen / vacuum line to do this work, the problem is that you are making a polymer. If you are trying to make a long chain polymer then if a small fraction of the repeat groups are changed then you will have a very different chain length and the properties will be very different.
I would suggest sparging the mixture with argon before you add the catalyst to get the oxygen content down as low as possible before you heat the mixture up. One option would be to bubble the thing with argon at room temperature for an hour or so, add the catalyst, carry on bubbling with the argon and then start to heat up.
After the reaction time, I would allow the mixture to cool and then I would tip it into water. The sincere hope is that the majority of the DMF will remain in the water while the polymer will not. I would then redissolve in dichloromethane and then use methanol as an antisolvent.
You might also want to consider using electrochemistry as an alternative to the Pd chemistry, I think it might be possible to make a polythiophene by gentle oxidation on the anode. I suggest you read about the work of Karl Ryder, he has got into deep eutectic solvents now but when he was in Aberdeen around 2000 his group there were making things like polythiophenes.