Hello,
This is going to hit a bunch of different questions that have come up over the years that I missed. Sorry!
I don't know about any possible changes at the SQL level because I haven't worked with RDBMS for years. If your RDBMS has a 'spatial' component, there's likely a function like 'project' or 'projection' that should do the equivalent. It might even take WKID numbers. Ah, check out the Microsoft SQL Server Spatial Tools. Actually, from that topic there's a link in the Tip that takes you to a GitHub opensource set of Spatial Tools.
The IOGP (absorbed EPSG years ago; EPSG name was kept for recognition purposes) Guidance Notes related to coordinate reference systems, geodesy, coordinate transformations/operations are available or linked from this page. The one you want if you're going to implement the math of a map projection is 7-2. Currently, it's available from the IOGP bookstore, but it's free. You just need to fill out your email etc. You might get some emails from IOGP; but you can unsubscribe.
re: NAD27. NAD27 uses Clarke 1866 versus GRS80, so you would need to change the semimajor axis and the semiminor axis OR the flattening value, depending on what is being used. Unfortunately the conversion between NAD83 and NAD27 in the US uses a grid file and would be quite a bit to implement. I've never done it myself.
There are some 'equation-based' datum transformation methods but the ones between NAD27 and WGS84 (rather than NAD83) are not very accurate.
Melita