Many thanks to those folks that responded.
I wanted to post my final solution so as to help others stuck in the morass of getting credit cards accepted on their site.
First off, some explanation.
First Data is a huge credit card processing company. They sell their services through many channels. This is important to realize since the initial contact point with First Data makes a difference on how or whether you'll be able to take credit cards.
The same is true of Authorize.net. Both companies have leagues of highly competitive salespeople that make a commission on any account they bring in.
In order to get credit card processing you need *two *types of accounts. Yes, two, not one! One is a gateway account and one is a merchant account or underwriter's account. The gateway is the vehicle that takes the cc data and handles the back and forth between your site and your customer. The merchant account is essentially loaning your website money for microseconds and/or guaranteeing that the customer's credit card, once verified as valid, is good for the purchase, and/or guaranteeing a charge back will be covered in case you default.
When I got completely frustrated with the lack of support from Authorize.net, I closed my account there and opened an account with First Data; they mistakenly created a GGe4 account for me. After a week or so of futzing around there I found the number and contact information for LinkPoint/Ignite. I called LinkPoint (866) 913-3220 and spoke with Oscar (ext. 803). LinkPoint is a reseller of *both *First Data and Authorize.net. As far as I could determine, LinkPoint does not do any cc processing themselves.
Oscar at LinkPoint explained to me the difference between the gateway and merchant accounts and pointed out that, at present, there is a bug in the First Data GGe4 suite that makes it unworkable with Zencart 1.5.x out-of-the-box. In other words you need to do some hacking to get GGe4 to work.
After closing my GGe4 account (they cannot be converted), I reopened a new gateway account through LinkPoint/Ignite with FirstData, i.e. Oscar. It is their plain Global Gateway account, not the GGe4(!) Oscar then set me up with an Authorize.net **merchant **account. It took about three days, start to finish (compared with two months with my prior attempts). Once I got the confirmation email, Oscar called Authorize.net and one of their people and Oscar conference called me and waited on the phone while I set up the various keys. Only after I had successfully completed a test purchase did they get off the phone with me. It's been about a week and things are smooth as pie. My customers are using credit cards, sales are up, and I get a little email when a charge is successful.
When I compared the pricing (about $29/month + 1.99% transaction fee + $0.23) this wound up being the cheapest way to go that I was able to find; there may be something cheaper out there, but at least I'm finally up and running.
Note that the date of this post is late April, 2014