So then once you've created your Invoice attribute, and its three options:

a1o1 = Invoice 1
a1o2 = Invoice 2
a103 = Invoice 3

So your link would look like this:

/cart/add/e-p43_q1_a1o2?destination=cart

(keep in mind the values will probably be different in the database - you'll need to remember the IDs of each attribute and combo, either from the Edit Attribute screen or from the uc_attributes_options table)

Or if there are additional values you need to grab, you're better off (for now) writing a Contrib that grabs them from the query string like this:

/cart/add/e-p43_q1_a1o2?destination=cart&invoice=foo&option=bar or something ... still unsure of what you need the I delimiter for but I trust you'll be able to figure it out