The key word in the summary is "legacy". This indicates that there is a large code base that the current developers are not too familiar with (deep knowledge, staff turnover causes this). This causes an organization to fear change due to the related complexity of changes and potential regression bugs. I'm going to guess that there aren't large, mature suites of unit and regression tests.
So I believe you have:
1. Complex code base without a lot of deep developer knowledge of the innards.
2. Fear to change things too much due to complexity and the possibility of introducing bugs.
3. Do not have effective, wide coverage testing implemented.
But, you also have good knowledge of Perl and the architectural elements that compose the system (server software, external libraries, etc.). That knowledge is very valuable and shouldn't be dismissed just for the sake of changing the base language of a system. And you have a working system. How many person years of development have been put into it? Are you willing to spend that much time on the replacement (do you think a replacement could be built in less time, and if so, why?)?
As well, rewriting large admin systems is very risky. I've personally seen two such efforts fail, a 100% failure rate from my personal experience (both had budgets over $5 million, one was over $40 million). Here's an article on this topic:
Consider keeping the existing system, but embarking on a long term (years) modernization/re-design/improvement effort to make the system more modern (ie. easier to work with). Focus on small, non-breaking changes that can go out with regular enhancement promotions (the modernization effort should be able to stop at any point, with any improvements to the system staying in place - this allows for tight budget control and financial risk mitigation). Hire a good application DBA to perform analysis and recommend changes to the data model. Hire a good software architect or bring in architectural consultants that can bring a different perspective to the understanding of the application, its goals, and how it could be improved.
Here's an article on approaching IT projects in a "Small and Simple" manner: