Let me offer three projects that did low-cost entity mark-up in my own experience which might be helpful.
The Civil War Governors of Kentucky Digital Documentary Edition had transcribed correspondence in TEI-XML created using a combination of DocTracker and Oxygen. These were available for further mark-up in an early access website (based on Omeka, with the documents lightly converted into HTML) as well of in XML source residing in a Github repository. Their goal was to mark up the people, places, organizations and geographic features mentioned within the documents, to identify and document those entities, and to connect the references within the documents to the entries on the entities themselves.
We had graduate students use Hypothes.is to mark up the entities within each document on the Early Access site. We then wrote an open-source system  to programmatically ingest the Hypothes.is annotations and present them for identification and documentation. We are in the very last stages of the project now, publishing the entities, their biographies and bibliographies, the links between documents and entities, and the network visualization of entities and their relationships. You can see more detail about the project at the presentation we gave at DH2017 this year.
I don't know enough about your project's resources, but Hypothes.is was an easy, inexpensive way to do the mark-up itself, and if installing Mashbill (and modifying it to remove the CWGK-specific code) is too much, you might ask your users to put URIs for entities hosted elsewhere into the annotation bodies.
FromThePage is an open-source collaborative transcription and annotation platform I developed to do almost exactly what your project is attempting. Users are presented with document facsimiles on a webpage and transcribe them into a data-entry box next to the facsimile image. The mark-up allowed is limited compared with the richness of TEI, but the system is optimized for entity tagging, identification, documentation and indexing. Users use wiki-links to mark up entities mentioned within a transcript, specifying a canonical name for the entity and the verbatim text within the document referring to it, as [[canonical name|verbatim text]] (e.g. [[Sally Smith Jones (1756-1823)|Rev. Jones wife]]. When users save a page containing linked subjects, a database record for the subject is created if it does not already exist, and an index entry created linking the page to the subject. All these are visible as HTML links and are transformed into rs and person tags in the TEI export.
I am biased, of course, but I'd think this platform solves the use cases you've described. I'm not sure how you'd convince your transcribers to move from Word to the web, however.
Another option might be to cut-and-paste the existing transcripts into MediaWiki sites like pbworks or wikia. The transcripts could be linked to articles about subjects using wiki-links (as in FromThePage). This would be pretty low cost, but the big challenge there would be in getting the data back out again, so you'd want to figure that out first. You'd also face the challenge of getting your users to start using the web.
Best of luck,
 Early Access publication: http://discovery.civilwargovernors.org/
 CWGK description of Mashbill: http://discovery.civilwargovernors.org/mashbill
 Source code for Mashbill: https://github.com/CivilWarGovernorsOfKentucky/Mashbill
 "Beyond Coocurrence: Network Visualization in the Civil War Governors of Kentucky Digital Documentary Edition" http://manuscripttranscription.blogspot.com/2017/08/beyond-coocurrence.html
 Commercially hosted version: https://fromthepage.com/
 Source code for FromThePage: https://github.com/benwbrum/fromthepage
 More detail on wiki-links at "Wiki-links in FromThePage": http://manuscripttranscription.blogspot.com/2014/03/wiki-links-in-fromthepage.html
 See links at https://fromthepage.com/yaquinalights/1871-1900-yaquina-head-lighthouse-letter-books/vol-439-cook-appt-1875/display/17170
Ben W. Brumfield
Partner. Brumfield Labs LLC
Creators of FromThePage