You can to proof a number is positive by showing it is bigger than a square number.
I have no experience with elliptic curves, but I think it can be done using an RSA modulo.
Using RSA modulo, addition is easy g^a . g^b \equiv g^{a+b} \mod N, I don’t think we have to worry about overflow, because the trapdoor is unknown.
Proving a is positive can be done by showing g^{x^2}. g^y = g^{a}, where you provide a positive y and proof x^2 is a square number without revealing x.
To proof x^2 is a a square I want you use a double Wesolowski proof as shown here.
Let A_x = g^x \mod N
Let A_{x^2} = g^{x^2} \mod N
We will substitute:
x = B\lfloor \frac x B \rfloor + x \mod B
We use the following witnesses:
b_1=g^{\lfloor \frac x B \rfloor} \mod N
b_2=A_x^{\lfloor \frac x B \rfloor} \mod N
r=x \mod B
The verifier should check:
b_1^B.g^r \equiv A_x \mod N
b_2^B.A_x^r \equiv A_{x^2} \mod N
It is not very efficient, because we need a lot of witnesses: y,A_x, A_{x^2},b_1,b_2,r to just proof a is positive, but it seems to work.