The following information is only my view from a common sense approach and in some cases actual experience. All problems consist of components related to the actual problem so take one component at a time and when you are reasonably certain that the component checks out normal move on to the next component. THE BEST ADVICE that I have ever received from a friend is to ALWAYS do the cheapest things first! In this case it is LABOR! DO NOT WASTE YOUR MONEY UNTIL YOU ARE ABSOLUTELY CERTAIN WHAT THE PROBLEM(S)ARE!
Have you tried to set the accelerator at, let's say, 2000 rpm( use a piece of wood or something) while parked? Use a volt meter while at this rpm or any other for that matter and you should read a minimum of 14.1 volts and no less. Bench testing is fine but when it is actually installed and operating you may find some issues that bench testing will not indicate. While doing this without actually driving the car do the same exact problems occur?
You stated that some electrical components continue to operate but are erratic and remember that the Tachometer is electronic and not cable driven.
Most importantly of all is to literally remove, clean and reinstall EVERY ground wire that you can. Inconsistent grounding can lead to some of the problems that you are experiencing. If the headlights work but are not as bright then you are providing current to them. The same goes for the Tachometer.
Have you tried activating the starter with a remote starter switch(key on with panel lights on)?
Push starting could possibly, repeat possibly, be a defective battery even though it is new. Receiving 14 volts from the alternator does not mean that you are obtaining the correct voltage out from the battery. If you have the finances then purchase a Hydrometer from AutoZone(do not scrimp but also do not purchase the "state of the art" product either). When using the Hydrometer VERY SLOWLY allow the electrolyte fluid to enter the Hydrometer and repeat every cell a few times to obtain a consistent reading. This tool is a good investment and should be used every time you check the water levels in the battery(before adding distilled water). You can remove the battery caps on even "so called" sealed batteries and the electrolyte fluid will evaporate even in a sealed battery. The exception are the new GEL-FILLED batteries.
Remember that you are capable of fixing these problems yourself. You have the intelligence, common sense and just relax and analyze each component. You will find that you know much, much more that you may think.
Good Luck!
Mark
Postscript: You can fix these problems on your own with some patience and additional suggestions from others who access this forum and are very knowledgeable and experienced. I come from a family of farmers and we have a saying, "Use good old common Horse Sense"! Farmers can usually fix ANYTHING because they usually have little money to spare.
