pay for your current place and finance the BOL. here's the reason. if the economy goes really bad, you lose your jobs and are stuck filing bankruptcy, then you can protect all* of the equity in your main home, but not your BOL. in other words, in the bankruptcy, if you own your main home and have the BOL financed, then you can protect the equity in your main home and likely be able to keep the BOL if it's mortgaged w/ little equity - b/c there's no equity in it there's no motivation for the bankruptcy court to take it. conversely, if you own your BOL and owe on the main home, you will still keep all the equity in your main house, but you will lose your BOL - the bankruptcy trustee will take title and sale it.
*check w/ an attorney in your state, b/c the amount of equity you can protect varies.
if you pay off your main house, then your debt to income ration should be really low and if your credit is good you should be able to get a loan. another option is to see if the current owner of the BOL can carry the note either for 5, 10 or 15 years, whichever works for you depending on your retirement plan.