Toyota did change the design sometime in the 90's to require dash removal to get at the heater core. If this is still true for 1994 cars don't know.
You could attempt to flush out the core with water.
The core is connected to two pipes that exit through the firewall on the engine side. Hoses connect to the pipes then the hoses connect to the engines coolant system.
One hose has a valve installed to control coolant flow through the core. The valve is typically close to the fire wall.
Access to the hoses at the firewall/pipe location is often difficult due to other parts being in the way. Might find an easier location to break the hose connections. Once done, make sure the valve is open (assuming you did not break the hoses at the firewall). Then use a garden hose to attempt to run water through the core.
Watch the water exit the other hose for debris and the point where the water begins to flow freely (assuming it frees up).
Not sure what direction the hot water runs through the core. Might be through the valve. Ideally you would want to apply the hose water in opposite direction of the water flow to back flush the core and debris out the same way it came in.
There might some chemicals you can use. An internet search may be helpful. This problem has come up before.
Removing the dash is a very time consuming job, suggest you do your best to flush out the core.
Suggest in the future to not use any chemical treatments in the cooling system, they tend to cause more problems then they solve. Use clean water from a garden hose to flush the system.