Deductions & credits

It's my husband's pension (Swedish social security) and he is a permanent resident Green card holder. Yes, I am trying to figure out the best way to report it. Substitute 1099R/4852 is easy, and I report the income and also report that zero is taxable. This is because the US-Sweden tax treaty states that it's only taxable by Sweden. So... I can simply report it, pay no US tax and do not claim foreign tax credit. Using this method my refund is $1254. And, a drawback is that I have to print and mail file, which is a giant pain because I file in three states (I have some rental properties). The other way to handle it is to report the income under "other reportable income." Here I report it as taxable and claim the foreign tax credit. I think that gives us a dollar for dollar credit up to the amount of what the US tax would be. It's less than the Swedish tax but whatever. If it nullifies the US tax then that makes it essentially untaxed income in the US, and the difference is accrued as a credit that carries over. Using that method my refund is only $383, but the TT summary shows a $2000 credit was used. (I cannot see how much is used this year and how much is carried over to next year as I'm using TT online.) The problem I am trying to work through is if I report the income and claim it as non-taxable by treaty, I get a bigger refund but am I missing out on a credit that carries over for 10 years and may be worth a lot more if I can actually use it? If I use the other method and accrue a bunch of credit, that might be a lot more money -- if I can actually apply it in future years. I'm not sure how exactly it would be applied (to offset what kind of taxes -- and do I have that kind?) so I cannot figure it out. In the future I will sell off rental properties, cash in investments, start drawing my IRA, etc -- all incurring taxes, I suppose? that could be offset by my carried over foreign tax credit. I have $7000 from last year (husband sold a lot of Swedish stuff and had a big tax bill) and if it's going to be a few thousand annually from his pension then that seems like a lot of credit and worth more than getting a bigger (~$900) refund this year. I just don't know if my facts are straight about how the credit works!