Notation conventions for superscripts and subscripts
This is only partial answer since your question is quite broad but in my work I had similar problems. 

When ti comes to optimal values and derivatives I choose to use Leibniz's notation as it does the job quite nicely:

instead of writing this $\pi^{'*}$, I would write this $\frac{\partial \pi^*}{\partial x}$ or if you like it more  $\frac{\partial }{\partial x}(\pi^*)$, sure it takes some time to type out but in my humble opinion it looks quite good. I try to use Leibniz's notation any time there are some other superscripts or subscripts (as with multivariate function even derivatives with subscripts can be problematic).

For conditions consider maybe notation borrowed from statistics so instead of $p^{*,\alpha =1} $ I would use $[p^*|\alpha=1]$

Regarding those numbered solutions, I was once told by older scientist, during my internship at one research institute, that when  you have one letter subscripts you can just put them without comma but if one of the subscripts has multiple letters always put comma so for example $x_{itj}$ is fine but when I need to put $t-1$ I would put it as $x_{ij,t-1}$ (to be honest I have no idea to this day if there could be some issue with this but so far nobody complained - not even at  conferences/workshops where I was presenting my work, nor any referee - although I dont have that many published work yet as I am very young researcher, so maybe take that as a caveat regarding my suggestions).