I already mentioned in several posts my simulator
NL5, which would be a good tool to be used instead of (or along with) what you call "hand calculations".
The idea of this simulator is that it is using very simple "generic" models: ideal diodes and transistors, OpAmps, switches, R,L,C, V and I sources, and much more. At the very beginning of the project, when you just estimating how schematic works, you don't need specific models yet, or may be you even don't know what real components exist at all, so you just use a "diode" with two states: On and Off, OpAmps with an infinite gain and bandwidth, etc. This is exactly what you do in your head or on the paper, but all the calculations are more accurate, plus you have all the graphs, you can easily modify schematic and change parameters, etc.
When you're done with estimation, you can switch to simulators with real component models (if you trust the models...) such a LTSpice, Tina, MicroCap, etc., to do detailed analysis of the schematic.
Thanks.