Hallo 
The 1000 dlogp evaluations in NUTS is an upper bound. This is controlled by the max_treedepth argument, the max number of evals is 2^max_treedepth, and that has a default of 10. Usually, the number is much smaller. And if it does get that large that means that the posterior geometry is really bad (so for instance if you have a funnel or if you have very strong correlations in the posterior).
I’m afraid a uniform doesn’t work as expected as the sd_dist argument of LKJCholeskyCov. This is a pretty unusual special case. Usually we completely avoid any parameter points by mapping constrained distributions to an unconstrained space, but in the case of LKJCholeskyCov we sidestep that machinery unfortunately (I guess it would actually be good to raise a warning here…).
Why do you want to have a uniform distribution here? There might be other ways of achieving what you want that avoid that problem…
I’d typically use a HalfNormal or possibly a Gamma distribution for those parameters. (But this is hard to make general statements about that).
500 tune and 500 draws is a bit on the low side. Usually the default of 1000 each is pretty decent.