This procedure is for cases where you made a mistake forming an entity, in this case an LLC, and you'll need to form a Corp in it's place.
This procedure is used if you did NOTHING with your LLC, and you want to form a corp in it's place. You'll notice the LLC dissolution fee is $60.00, and the Corp formation fee is $135.00, so if you see a CPA, he would at least have to spend $195 in fees on your behalf.
Usually, CPA's in my area charge fees of at least $100/hour or up, and the above does not seem complicated, something you can do yourself. I wouldn't pay more than $200 in professional fees for someone to do this. Add this to the state fees, maybe $400, tops.
I haved formed corp entities, and dissolved some, but I never used the procedure described here as the "1-2 filing", but it does not appear that complicated. The article is from year 2007, so you might double check the current fee schedule on the NYS Department of State WEBsite.
Now, I have dissolved a C Corp myself following the directions on the NYS DOS Website, downloading their forms, and paying the fees online by credit card.
As Bubba pointed out to you, there are formalities after the formation of the Corporate entity, the initial meeting, the election of officers etc., and I'm not sure if most CPA's cover that. The service I cited earlier does all of this in the formation for a total of $164.95, including the book, seal, writing up the initial meeting and election of officers. See link:
BTW, on the question of maintaining corporate formalities, the above firm provides a service for doing that as well, for an annual fee, which includes writing up an "annual meeting" for you, keeping a copy at their (your lawyer's) office, and a hot line for answering questions.
You can try calling them and see if they can do a "1-2 filing" mentioned above.