Instead of the Treasury Index, the new High Cost rule is based on the comparable APOR. Is it still based on the rate for the 15th of the month prior to application date?

It depends on what type of transaction. See below.

(3) Determination of annual percentage rate. For purposes of paragraph (a)(1)(i) of this section, a creditor shall determine the annual percentage rate for a closed- or open-end credit transaction based on the following:

(i) For a transaction in which the annual percentage rate will not vary during the term of the loan or credit plan, the interest rate in effect as of the date the interest rate for the transaction is set;

(ii) For a transaction in which the interest rate may vary during the term of the loan or credit plan in accordance with an index, the interest rate that results from adding the maximum margin permitted at any time during the term of the loan or credit plan to the value of the index rate in effect as of the date the interest rate for the transaction is set, or the introductory interest rate, whichever is greater; and

(iii) For a transaction in which the interest rate may or will vary during the term of the loan or credit plan, other than a transaction described in paragraph (a)(3)(ii) of this section, the maximum interest rate that may be imposed during the term of the loan or credit plan.

Right. But what APOR date are we to compare that rate to? The 15th of the month prior to application?

Harpo, look to the commentary to the reg under .32(a)(1)(i) paragraphs 1-4. It refers to .35, so appears the comparable APOR will be determined the same way as it is for HPML.
BOL updated Reg
It will hopefully be fairly easy when they update the FFIEC calculator.

Are interim construction loans covered or are they exempted as temporary loans?

Paragraph 32(a)(2)(ii).
1. Construction-permanent loans. Section 1026.32 does not apply to a transaction to finance the initial construction of a dwelling.