I’m happy to share that we do have a subscription to Springer journals, which covers more than 90% of the Springer journal titles. You can search these journals directly at http://link.springer.com/.
Regarding Taylor & Francis journals, we have subscriptions to a few of the T&F titles, but not a large number. We explored a subscription to a larger set of T&F journals a few years ago, but the cost was too large for our budget. Note that our EBSCO databases do include a significant amount of full-text T&F journal content, usually up to the most recent 18 months (for the newest material, you can use Interlibrary Loan. We analyze Interlibrary Loan statistics for journal requests on an annual basis to see if there are highly-used journals for which we do not have subscriptions.)
If you’re interested in specific titles from these publishers, please send an e-mail to firstname.lastname@example.org or contact your subject librarian.