I am creating a class assignment for a senior English Lit class in which I would like students to take on the role of various Romantic authors:...

Good, creative lesson strategy. The essence of your question seems to be: What would be some good questions to ask a Romantic, so that the student can think like a Romantic in answering, thereby tapping into the Zeitgeist of early 19th century England.

However, if we ask questions about the modern-day world, such as “What do you, Wordsworth, think should be done about loss of species due to over-lumbering, over-fishing, pollution due to burning of...

Good, creative lesson strategy. The essence of your question seems to be: What would be some good questions to ask a Romantic, so that the student can think like a Romantic in answering, thereby tapping into the Zeitgeist of early 19th century England.

However, if we ask questions about the modern-day world, such as “What do you, Wordsworth, think should be done about loss of species due to over-lumbering, over-fishing, pollution due to burning of fossil fuels, etc.?” we will be confounding history, since the Romantics will have no solutions, merely laments.  So, the idea, "I would like to have the students address contemporary issues through the lens of the author" is a little vague.  Are you thinking of question like these? "What do you think of the poetry of rap?  Do you think Taylor Swift is a Romantic?" 

If we ask them sociological questions, such as “What do your non-Romantic contemporaries think of your attitudes” we might get a little insight into how comfortable or uncomfortable the Romantics were in that environment.

If we ask interpretive questions about a canon or a specific work, the role-playing aspect of the exercise is wasted.

How about questions about their personal creative process – how did Wordsworth come up with his daffodil imagery after starting with “I wandered lonely as a cloud”? That is, how did they work from an idea to a finished product (a question we often ask of song-writers)? Another fruitful question type might be “How did you get along with your fellow poets (for example, how did Wordsworth and Coleridge actually get along?  Or "Did Romanticism change much during your lifetime?" (An interesting sidenote:  Of the five major poets, the first poet to be born was the last one to die. In fact, their birthdays-deathdays fit into each other like Kachina dolls.)

Finally we might get good pedagogical value out of asking them “What work of yours has been unfairly neglected? What poem would you want to be anthologized more, and why?”