Rhodium, I see your reason for concern: esters of sulfonic acids also undergo elimination by treatment with a base (or by heating). It seems that we have to find the reaction conditions that favour nucleophilic substitution and minimalize the extent of alkene formation.
My impression is that you don't have to worry much about steric hinderance with this reaction.
Take a look at this:
A mixture of 5.7 g (0.03 mol) 3-methyl-N-phenyl-4-piperidineamine HCl and phenyl-2-propanol methanesulfonate (7g, 0.033 mol) in i-BuCOMe (300 mL) was stirred and refluxed for 48 hours. The mixture was allowed to cool and extracted with H2O, the organic phase dried (MgSO4), and the solvent removed in vacuo. The residue was crystallized as the HCl salt from i-Pr2O - i-PrOH to give 3-methyl-1-(1-methyl-2-phenylethyl)-N-phenyl-4-piperidineamine dihydrochloride (10.5 g, 92 %).
It seems that the steric hinderance & the heating didn't cause elimination.
As a side note: bis(tetra-n-butylammonium)oxalate is the reagent of choice for inducing tosylates to undergo elimination rather than substitution.
The procedures above uses TEA/MsCl and Pyr/TsCl, but why not use TEA/TsCl? There is probably a reason, but as I don't know about it, I would be very glad for a little elaboration on the topic.
I know that they use pyridine as a catalyst to make the ester between an alcohol and an acyl chloride. Pyridine catalysis involves the initial formation of an acyl pyridinium ion, which then reacts with the alcohol. Pyridine is a better nucleophile than the neutral alcohol, and the acylpyridinium ion reacts more rapidly with the alcohol than the acyl chloride. Furthermore, the piperidine captures the HCl that is formed during the reaction.
I don't know this for sure, so don't shoot me if I am wrong, but I guess that it would be the same thing for the tosyl chloride. Tosyl chloride is an (anorganic) acid chloride after all. First pyridine reacts with the p-toluenesulfonyl chloride, and then the alcohol reacts with the tosylpyridinium ion. Since pyridine is used as solvent, there is more than enough of that nasty stuff to capture the liberated HCl.