Article II, section 2, clause 2; and listing(s) of relevent treaties

Question

I have some information relevant to the Panama Canal on my website. I also have, in a database, the US constitution broken down by clause which includes:

[the President] shall have Power, by and with the Advice and Consent of the Senate, to make Treaties, provided two thirds of the Senators present concur.

I am now trying to tie together the 'Torrijos–Carter Treaties' & const. clause with a list of treaties that meet the conditions of this constitution clause. Simply stated, 'Where can I find (or compile) a list of Treaties that meet this constitutional condition?' It is my understanding that both of the 'Torrijos–Carter Treaties' are this type of Treaty[1]. I have found the text[2] of these treaties, that are titled:
1.'The Treaty Concerning the Permanent Neutrality and Operation of the Panama Canal' ('Neutrality Treaty')
2.'The Panama Canal Treaty'

I did find this pdf[3] from the US DOD, titled 'A List of Treaties and Other International Agreements of the United States in Force on January 1, 2013', but I am not sure it is complete with respect to my search - or I don't understand the referencing system in this document. This list includes on page 224 in 'PANAMA'/'CANALS' section, the following:

"Treaty concerning the permanent neutrality and operation of the Panama Canal, with annexes and protocol. Signed at Washington September 7, 1977. Entered into force October 1, 1979, subject to amendments, conditions, reservations, and understandings. 33 UST 1; TIAS 10029; 1161 UNTS 177'

While this sounds like item #1 from above, I am not certain if it is (or is not) a reference to #2(?). Scanning the document for 'Panama Canal Treaty' does produce a few results that reference the treaty, but no specific treaty of the same name is listed.

Again, 'Where can I find a list of Treaties that meet this constitutional condition (of which the "Panama Canal Treaty" I speculate is one)?

Footnotes:
1."The United States Senate advised and consented to ratification of the first treaty on March 16, 1978 and to the second treaty on April 18 by identical 68 to 32 margins." -Source: Wikipedia
2.http://lcweb2.loc.gov/frd/cs/panama/pa_appnb.html
3. http://www.state.gov/documents/organization/218912.pdf

Answer 1

That "List of Treaties" from your State Department reference includes this language in the foreword:

The term “treaty” as a matter of U.S. constitutional law denotes international agreements made by the President with the advice and consent of the Senate in accordance with Article II, section 2 of the Constitution of the United States.

So you correctly found an exhaustive list of treaties. Note that it may not be complete with regard to other international agreements, executive Memoranda of Understanding, or similar arrangements that did not follow the Senate ratification route.

The vaguely named treaty you cite regarding the Panama Canal is indeed Torrijos-Carter. It was signed September 7, 1977, matching the State Department list with your Library of Congress citation, as well as the Wikipedia entry.