Keras Looping LSTM layers

Question

I am trying to build a model which is basically sequence to sequence model but i have a special encoder namely "Secondary Encoder".

Timesteps in Secondary Encoder = 300

this encoder has a special property, in essence it is a GRU, but at each timestep the hidden state produced by the GRUCell is needed to be altered, it is needed to be Added with another variable and then this combination(new hidden state) is passed on to the next GRUCell which uses this as initial_state........this thing repeated 300 times.

As 300 GRUCells are required (one for each time step) it is not feasible to hard code each of the 300 layers and create the model. So, I need help to figure out how to write a loop to implement this thing in keras or maybe how to create a custom Layer (if this is a better choice).

what I thought (pseudocode) :-

here alpha is the variable that I was talking that i want to add

x = Input(shape=...)
encoder_cell = GRU(10,return_state=True)
init_state = xxxx     //some value to give as initialiser to first GRU cell
for t in range(300):
    _,hstate = encoder_cell(x[t],initial_state = init_state)
    init_state = hstate + alpha

model = Model(inputs = x, outputs = init_state)

will this work ? will the model be able to interpret that it needs to loop 300 times at each training example?

The model is quite big it has skip connections and lots of other things that's why i need your help to figure out this subset of my problem before i implement the rest, and please ignore the syntax, this is just pseudocode.

Also, I need to call this model again n again, so i think the iterative way will slow down the process by quite a lot right?