The introduction to the SAQ A-EP Document (PDF) reads (emphasis mine):
Before You Begin
SAQ A-EP has been developed to address requirements applicable to e-commerce merchants with a website(s) that does not itself receive cardholder data but which does affect the security of the payment transaction and/or the integrity of the page that accepts the consumer’s cardholder data.
SAQ A-EP merchants are e-commerce merchants who partially outsource their e-commerce payment channel to PCI DSS validated third parties and do not electronically store, process, or transmit any cardholder data on their systems or premises.
Your servers receive cardholder data (albeit via an API rather than through an interactive web-page) and processes cardholder data (to tokenize it before forwarding to a third-party site). Therefore my reading of the above is that SAQ A-EP is not applicable.
The use of the word website in the first paragraph is, presumably, to cover "normal" websites that hand both the acquisition and processing of cardholder data to another party: for instance by opening a new window or embedding an
<iframe> in their webpage (and where the contents of the window/iframe is provided by the third-party and not your servers).
While one could debate whether "website" in the first paragraph includes a non-interactive API, I think that is irrelevant1. The second paragraph does not use "website" – it talks only of "systems" and "channels" – so would unambiguously apply to your situation. Since you do process cardholder data, you cannot be an "SAQ A-EP merchant".
Therefore, of the two, the SAQ D questionnaire would apply to your situation2.
1 My strong suspicion is what really matters in the first paragraph (and this view is backed-up in the second paragraph) is the passage I highlighted, namely "that does not itself receive cardholder data". Even if your API is not considered a website, it does (or will) receive cardholder data, and therefore you would not be eligible for the (presumably less onerous) obligations of SAQ A-EP.
2 Note that the introduction of SAQ D (PDF) reads "SAQ D for Merchants applies to SAQ-eligible merchants not meeting the criteria for any other SAQ type.". Of the two SAQs you mention, you clearly (in my mind) don't meet the criteria for SAQ A-EP. However, according to Understanding the SAQs for PCI DSS version 3 (PDF), there are a number of other types. It's conceivable (though from a quick scan of the opening page, unlikely) that you could be eligible for one of those.