Adjusting Tiagra Front Derailleur FD-4700
Is it essential that I align the outer of the derailleur cage with the largest chainring before proceeding? 


Yes!


  Is there any chance I could avoid adjusting the limit screws?


Absolutely not! Unless you like having the chain fall off the rings. Having the chain come off between the crank and frame is at best a pain and at worst damages the frame. 

When you swapped in the new crank the derailleur adjustment should not have been too far off. It sounds like you just needed to adjust limits and indexing, but the height and angle were OK. What I would have done at this point was followed the Park Tool video, checking hight and angle, then setting high and low limits and indexing according to their procedure (referring to the Shimano manual for specifics for adjustments). You might have been able to do this without detaching the cable.

If you have detached the cable, or adjusted the position of the derailleur on the frame just work through the procedure from the start. I've done well with the Park Tool guide, the Arts Cyclery video seems a bit more specific to Shimano. Front derailleur adjustment is tricky, it's certainly harder to do than rear derailleur adjustment. Don't skip steps, that will just cause worse problems later.

BTW, I'm gratified that you followed my advice about upgrading the crankset :-)