Separating specific components of a PUREX raffinate
You have chosen a difficult challenge, a word of advice unless you are working in a nuclear site I would advise you in the strongest terms possible not to attempt a separation of radioactive things in your kitchen, basement, garden shed or some other home lab.

OK warning over, now the idea of adding flouride to create a percipitate of lanthanide (and post plutonium actinides) is a nice idea but it will make any further processing of these elements harder. I also worry that any traces of plutonium or other elements such as zirconium might become incorperated into the lanthanide flouride perceipitate.

I would suggest that you consider solvent extraction as the separation method, I would suggest that you consider the TRPO process chemistry from China. If you were to dilute the PUREX raffinate to reduce the nitric acid content to about 0.5 M, then shake the PUREX raffinate with about 30 % (v/v) of cyanex 923 in an aliphatic kerosene then you will have a organic solution which is a mixture of lanthanides, zirconium, iron and residual plutonium / uranium.

I would suggest stripping (back extracting) the organic phase with strong nitric acid, the plutonium, uranium and zirconium will stay in the organic phase while the lanthanides will go back into the aqueous phase.

In some ways a better alternative would be to use TODGA or a malonamide, a solution of one of these reagents in aliphaltic kerosene will extract the lanthanides from PUREX raffiniate without adjustment of the nitric acid content of the raffinate. You can then strip the lanthanides (plus the americium / curium) from the raffinate. These types of processes have been tested at ITU in their hot cells using PUREX raffinate formed from real fuel.

In some ways I would want to use dilute nitric acid as a stripping agent for the lanthanides from a diamide based process. You can then reextract the lanthanides from the dilute nitric acid with 30 % DEHPA (bis-2-ethylhexyl hydrogen phosphate) in kerosene. In turn back extract this new organic phase with nitric acid, if you are careful it is possible to get some separation of the lanthanides into the heavy and light lanthanides by selective stripping with different concentrations of nitric acid.

Another method which would work would be to use the TRUEX process chemistry from the USA, this is based on CMPO in tributyl phoshate modified kerosene.