Well... if you exclude canceled debt and do not reduce any tax attributes - the sale transaction will result a loss - and that would be double dipping - you may not take double benefits from exclusion.
The sentence from instructions you mentioned is not related to reduction of tax attributes - it simply mentioned two different types of exclusion and priority in which they should be applied. However regardless which type of exclusion is claimed - you still need to reduce tax attributes - in your case that is the basis of the property.
No need to be insolvent. Considering your situation - you do qualify to exclude the canceled debt as "qualified real property business indebtedness" No need to verify insolvency - still you will need the tax attribute reduction - means the basis should be reduced by the amount of debt forgiven.
Use Form 982 - www.irs.gov/pub/irs-pdf/f982.pdf - specifically - for rental property - check the box 1(d) - Discharge of qualified real property business indebtedness , and put the forgiven amount on the line 2 and on line 4 and line 10a. The line 10 is specifically to reduce the basis.
The disposition of the property is reported on Form 4797 - http://www.irs.gov/pub/irs-pdf/f4797.pdf - is to report the disposition of business property - rental property in your situation. To calculate your gain or loss - you will use an adjusted basis reduced by the amount of debt forgiven.
The gain of $37k will be treated as following:
$7k will be depreciation recapture and will be taxed as ordinary income
$30k will be taxed as capital gain.
Also - if you have any rental losses including carried over from previous years - they are deducted against your gain.