Using Specialize and compute_at efficiently

[ImageHandler]

Consider a function (func1) which contains sevelral sub-functions (func2, func3, func4 etc.). All these subfunction iterate over the image full image size. The structure of the functions are as follow :

Code snippet (consider c code)

func1(input, output, param1, param2, param3)
{
	if(param1 > 0)
		func2(input, output)
	
	if(param2 > 0)
		func3(input, output)
	
	if(param3 == 1)
		func4(input, output)
	else if (param3 == 2)
		func5(input, output)
	
	return output
}

(func2 or func3 or func4 or func5)(input, output)
{
	for i:0 to image.size()
		output[i] = some calculation on input[i];
}

Halide equivalent :

func1(intput, output, param1, param2, param3)
{
	func2_stage(x, y) = select(param1 > 0, func2(input, output), output(x, y));
	func3_stage(x, y) = select(param2 > 0, func3(input, func2_stage), func2_stage(x, y));
	func4_stage(x, y) = select(param3 == 1, func4(input, func3_stage), 
						select(param3 == 2, func5(input, func3_stage), func3_stage(x, y)));
}

Assume func2, func3, func4, func5 are already implemented.

-I have already written the halide code for this (all functions are written).
-I want to run it on HVX(Hexagon DSP) as target.
-From my previous experiences compute_at() will give a huge benefit in the latency.
-I have shown here only till func5 but there are many, and with many specialized switch statements

My Scheduling:

func2_stage
	.specialize(param1 > 0)
	.vectorize()
	.parallel()
	;
	
func3_stage
	.specialize(param2 > 0)
	.vectorize()
	.paralle()
	;

func4_stage
	.specialize(param3 == 1)
	.vectorize()
	.paralle()
	;

func4_stage
	.specialize(param3 == 2)
	.vectorize()
	.paralle()
	;

-What I want to do is use compute_at (so that temporary full sized buffers for func2_stage, func3_stage, func4_stage are not created) for every func, along with specialize to give vectorization benefit.
-But while building halide it say .specialize() can't be used with .compute_at()
i.e the following

func2_stage
	.specialize(param1 > 0)
        .compute_at(func3_stage, x)
	.vectorize()
	.parallel()
	;

What can be the best possible schedule for the above scenario?
Please help

Thanks!

[ImageHandler]

@abadams @steven-johnson @zvookin any help would be great. Thanks