There are many misconceptions about what will and will not work with LabView, and what you do, and you do not need to build a decent system with it.
First of all, as others have said, testing and measuring the road. No matter what you end up doing, the system you describe will cost thousands.
Secondly, you do not need to use NI equipment with LabView. For thermocouples, it is best to look at multi-channel or several single-channel thermocouple blocks - something that is read from a thermocouple and output to something like RS-232, etc. Examples are OMEGABUS Digital Transmitters, but many others exist.
Thus, you only need a breakthrough card with a large number of RS-232 ports, and you can develop your system as you wish. You can still use labview to receive data through RS-232, and then display, register, process, etc., but you like it.
Third-party signal generators will also work, for example. You can pick up the good ones (with GPIB connection) reasonably cheaply, and the GPIB can also integrate it into LabView. This is if you want something like a function generator, of course (pulses with cyclic loading, standard sine / triangle / ramp functions, etc.). If you are talking about generating an arbitrary signal, then this remains a rather expensive task (if $ 5,000 is our goal for the "expensive").
It also depends on what you need to generate the signal - if you are thinking about pilot signals, then again there may be cheaper and more reliable opitons. For temperature control, for example, separate hardware PID controllers are preferred. This will also take care of your thermocouple problem, since PID controllers usually also accept thermocouple inputs. Thus, you only need one interface (for example, RS-232) for an external PID controller, and you have full access to the temperature readings in LabView, as well as the ability to control the settings and PID parameters in one unit.
Perhaps if you could develop not only the system components as you currently planned, but also the functionality of the ultimate system, it might be easier to propose alternatives - not just alternative equipment, but an alternative system design in general.
edit:
Take a look at the Omega CNi8C22-C24 and CNiS8C24-C24 devices β these are DIN PID temperature and voltage measuring devices that will receive inputs from your thermocouples and strain gauges, process the inputs to the corresponding measurements and communicate with LabView (or whatever) through RS-232 .