Between the lines I read that you want to register a SIP extension via an API and place calls form that extension. Why cant you utilize an actual desk phone or end user soft phone as the calling party?
DMCC can cause a SIP desk phone or soft phone to place a call to another party. Am I right that you don't have an existing hardphone or softphone to use as the originating extension? If you do have an existing Avaya built SIP device to use as the originator, you can use a DMCC call control services against that extension in to place a call from the SIP phone to another phone number. There are a number of pre-conditions that must be met for this to work. There is no need to register a DMCC device against the SIP device if all you want to use are call control services (this may be the problem you speak of -- you can only register a DMCC device in INDEPENDENT mode against a SIP device AND the set of DMCC services is significantly reduced with such a configuration).
Please review these two FAQs.
https://www.devconnectprogram.com/site/global/products_resources/avaya_aura_application_enablement_services/support/faq/index.gsp#860 https://www.devconnectprogram.com/site/global/products_resources/avaya_aura_application_enablement_services/support/faq/index.gsp#880
Avaya CTI works with Avaya devices, thus you have to use an Avaya SIP desk phone or soft phone as your originating entity.
JTAPI will not help you register a SIP device. It is just another way of invoking the MakeCall() functionality already available to you in DMCC and TSAPI, but if MakeCall() is what you need, it can facilitate placing a call from a SIP station to a destination (but as I said above DMCC can do that as well).
You could use a DMCC H.323 device to originate the call and transfer it to the actual party (or conference it in and drop out the DMCC device at the right moment). Keep in mind that one of the two calls must be 'stable' before you will be able to complete the conference or transfer. By stable I mean past the point of having been answered.