Am I able to use FAR 5.202(a)(11), as an exemption for not synopsizing an option; even when awarded the purchase order was exemption from synopsizing the "proposed action" in accordance with FAR 5.202(a)(13) and the "contract action" in accordance with 5.301(b)(6)?
The exception you referenced FAR 5.202(a)(13) does require notice of proposed contract action through GPE (see excerpt below). Hopefully, the option that needs to be exercised was included in the notice at that time. If so, then yes, you can use FAR 5.202(a)(11) as your exception for not synopsizing the option. If it was not included in the original notice, I think you'll need to synopsize it in accordance with FAR 17.207(c)(4).
Excerpt from FAR 5.202(a)(13):
The proposed contract action-
(i) Is for an amount not expected to exceed the simplified acquisition threshold;
(ii) Will be made through a means that provides access to the notice of proposed contract action through the GPE; and
(iii) Permits the public to respond to the solicitation electronically;