Craig,
In general I think 2 invoices and 2 reminders in a matter of days is way too much too soon.
I don't have to send out too many invoices because I have auto checkout on my shop - however.. when I do send out the first invoice, this is what I put in the notes for them:
"Thank you for selecting this card. If you are still browsing through more of my items please feel free to take your time as I can always amend/update the invoice as required."
Usually payment comes through pretty quickly - or in some cases a few days, sometimes a week - no problem. But by having the above comments included in the invoice there is quite a stark distinction from what buyers usually expect on other sites, ie: payment demands within so many days. Not only that but you have subtly and politely introduced the option of them adding to the order (up-selling) and you have given them the confidence in you to do so.
The majority of the time the initial product purchased would be all they require. But the polite up-sell does work, last Sunday alone 29 items of mine were sold on up-selling using good old gentle communication to buyers. So not only did I sell more, I also got thanked by the buyers for giving them the option of adding to their order.
Also in general I wouldn't jump in with giving the buyer neutrals because they have a strike-through - there could be very basic reasons why eBid are doing a check. Although with the specifics of this case you mention, I happen to know of their account on other sites - which raises more than a few questions in my mind as to what is going on (but even that could be perfectly legitimate, although certainly bizarre).