Antoncho, your problem might be with mixing NaOH with the NaMeSO4. Wouldn't that tend to hydrolyze the NaMeSO4? Why not use NaMeSO4 alone in water and add the sodium salt of hydroquinone to it, reflux, steam distill, etc?
Also look at US patent 2490842 and this link (GB patent)
http://l2.espacenet.com/dips/bnsviewer?CY=gb&LG=en&DB=EPD&PN=GB646736&ID=GB++++646736A++I+
I think you're adding things out of order. One method might be as follows:
1. Mix methanol and H2SO4 to get a mixture of MeHSO4, MeOH, H2SO4 and H2O.
2. Pour mixture into water and add excess CaCO3 to neutralyze the H2SO4 and also form Me
2Ca(SO
4)
2.
3. Filter out excess CaCO3 which is insoluble in water.
4. Add a solution of the sodium salt of hydroquinone, heat and stir until reaction is complete.
5. Steam distill the dimethoxybenzene from the reaction mixture.
One problem would be figuring out how much Me
2Ca(SO
4)
2 is in the solution, but you can use an excess of it.
http://www.geocities.com/dritte123/PSPF.html