Chossing between regression models

This is the first time I attempt to use machine learning with Keras. In contrast to others I need to use one of the disadvantage of such algorithms.

I need a function that accepts an angle and distance to an object and output a new angle and power (imagine aiming for an object with a bow for example and the algorithm tells me how far up my arm should go and the bow’s power).
There’s nothing predictive in this configuration. I will generate a large set of 4D (input,output) data with every possible case. I want the AI to "evaluate" some inputs and return the corresponding outputs for that set of inputs, in other words to remember the data and output the same numbers.

I need an AI for this task because I need smooth values between inputs values it has never seen (limited interpolation)

I have used two models:

model = Sequential()
model.add(Dense(12, input_dim=2, activation='relu'))
model.add(Dense(24, activation='relu'))
model.add(Dense(24, activation='relu'))
model.add(Dense(24, activation='sigmoid'))
model.add(Dense(2, activation='linear'))

Which now I know is incorrect because Sigmoid is used for binary classification. Still, it works! I end up with a mse of 4. I did not manage the get the same loss with all-ReLu layers with the same # of epochs.

model = Sequential()
model.add(Dense(12, input_dim=2, activation='relu'))

model.add(Dense(24, activation='linear'))
model.add(LeakyReLU(alpha=0.1))

model.add(Dense(24, activation='linear'))
model.add(LeakyReLU(alpha=0.1))

model.add(Dense(2, activation='linear'))

This models has a loss of 5.43 after 500 epochs and seems to stabillize here.

Note:

1. I am forced to retrain the model because I generate the training data very fast. I need to stay with a model that will keep going reduce its loss.
2. Normalization is worse than anything I have seen.
3. Because my model should be sensitive to different very close inputs, I tested with batch values from 5 to 2.
4. My dataset is currently 1100 of lines
5. This model will be trained very closely to the data I give it. It should not matter how many lines I feed it because I don’t want prediction or generalization. I want the AI to output what it has seen for a corresponding set of inputs. That would mean overfitting the AI to the maximum until it reaches a very low loss. Then I can test it for exactly those values it was trained on.

Should I continue with the first model? Does it make sense to use the Sigmoid layer? How can the second model be improved?

Sample of my data:

theta[-90,90], distance [0,40],  theta_output[-90,90] power[0,1,2]
0.0,8.696802,0.25688815116882324,1
-1.990075945854187,5.455038,11.56562614440918,1
-56.81309127807617,3.1364963,-53.07550048828125,1
-38.21211242675781,4.718147,-32.30286407470703,1
-33.828956604003906,5.163292,-35.61191940307617,0
-27.64937973022461,6.182574,-25.107540130615234,1
2.8613548278808594,13.922726,-2.3708770275115967,2
-8.812483787536621,14.951225,-3.919188976287842,2
0.0,21.448895,-3.9320743083953857,2