Since you guys are talking about paying taxes, I a

Since you guys are talking about paying taxes, I assume your warrants are in a CASH account. And if it is, then it should be Marginable. If you want to exercise and and pay No Taxes then exercise them at Cost ($3.44 + the price you paid.) and sell what you have to, to pay the bill. The cost basis for the new shares will probably start on the day you exercise them. To pay less taxes on any gains from here, you would have to hold them for a year to pay lower LT gains.

But why worry about paying taxes.
Pay and enjoy your good fortune!