Question: Transport delay using DynamicSystems?

I have a problem where there is a true deadtime due to a transport delay.  The delay is in the order of 8 minutes as a fluid flows very slowly down a tube.

I've fit an expression to some measured data and have found the following expression

I'd like to work with this using the Dynamic Systems Package, so I'm trying to build a system from the time-domain expression.  When I try to use the inttrans:-laplace function to convert to the s-domain, I get an overflow.  If I manually express this as a Laplace transform and try to make a system and do a step response, I get this, with an error that "transfer function(s) are not rational-polynomial(s) in s"

Is a delay supported in the Dynamic Systems Package?  If so, could you provide guidance on how?