. What steps do I need to do before taking it to shop?

Question edited for clarity add maker and turn question around.

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Hey Dave, will the starter turn the engine over at all?? Just because the battery is showing 12V+ does not mean it has any amperage (amperage is what starts your engine - NOT voltage)
Your battery may be getting old... take it to O'Reilly's, AutoZone, or your local battery shop and have the CCA (Cold Cranking Amps) checked, then you will know the real condition of your battery.
Once you do this, if it still won't crank, reply back to me on here.

Have your batteries CCA checked.. (Cold Cranking Amps).. take it to a battery shop or autozone or Oreilly's.. they can check it..this is what makes your engine crank..NOT voltage.... and how do you know the starter is good?..

This is not enough info to start. ..Hold the palm of your hand over the back of the carb and make sure its sealed against it... You need a helper to do this properly. The engine should pull on your hand inwards... if not....??
Did a shop or factory trained mechanic do the work? Are the reed valves able to open and stay closed? What does the compression gauge read? If you don't have one, beg borrow, buy, and/or take it to a shop and pay them to check it. Check it with the throttle wide open... with new piston and rings it should pump over 120+psi. ..easily.
Have the compression checked and then repost with the results.
Thanks!

Big Red Service Manual 2009 2012 Divided downloads You can get the entire manual here. It is in sections so you'll have to do several downloads.

A professional shop will charge from $85 to $110 per hour..depending on location...ask how they determine the charges... ALL manufacturers have a flat rate manual that SHOULD determine how many hours to will take...( When I was working in a shop.. I was usually about 1/2 hour behind on full overhauls..and could usually beat the flat rate on electrical issues)..
Should be able to get out for about 4 - 5 hours..depends on if they have to remove the engine first...engine removal/reinstall is about another hour.

It Is not getting lubrication to part of the engine. Take it to a shop before you destroy the engine.

It blinks because its telling you have misfires. Look into getting a full tuneup.

Do I take it the engine is already stripped to establish the fault. I've owned several Honda's and never seen this fault. If its in bits a good motorcycle engine shop could do it and recut the seat but only a search of parts books would tell you if Honda used a motorcycle head. Saying that, Honda do appear to use modified bike engines to power quads. New crank cases built onto a previous barrel and head.
Call a Honda specialist or a quad shop who may have already worked it out for themselves. Check out quad forums as well?

1. How could you tell it wasn't getting enough fuel in the "power band?"..i.e. the upper rpm range...?
A "power band" is simply the RPM range where the engine makes the most power.. it is more pronounced on modified two-cycle engines.. it is NOT something you can buy or have "installed".
Adjusting the float level only accomplishes getting more (or less) fuel in the carb bowls to make it available to the jets. >>The JETS are what (and ONLY what) gets the fuel to the engine!<<
Spark plugs are read to tell whether their is a need for a jetting change.. if you do not know how to do this - STOP tinkering with your engine-PERIOD!
You need a factory shop manual to get the necessary specifications of the ignition system,,(resistance values)...then and only then can you adequately check the wiring and related components...
What is a hot rod crank? I have built numerous banshee racing engines.. just wondering about yours.. $3000 in an engine.. it should have come with 34mm carbs, new head, ported cylinders, etc...jetted by the person that built the engine... if it didn't you need a new engine builder!!!
Do you live near North Alabama??