replacement - Change Operator Precedence of --> operator

I am trying to use --> operator with highest precedence

Unprotect[LongRightArrow];
LongRightArrow[obj_,property_]:=obj[ToString[property]];
Protect[LongRightArrow];

With this I can do basic operations like accessing properties of an association

In:=  obj = <|"a" -> {2, 3}, "b" -> 5|>
Out:= <|"a" -> {2, 3}, "b" -> 5|>
In:=  obj⟶a
Out:= {2, 3}

However when I try to access elements of list in obj-->a Part takes higher precedence. Same applies for operator ^.

In:=  obj⟶a[[1]]
Out:= Missing["KeyAbsent", "a[[1]]"]
In:=  obj⟶a^2
Out:= Missing["KeyAbsent", "2 a"]

Answer

How about overloading the LongRightArrow with a special rule for Part[...] as the second argument?

Unprotect[LongRightArrow];
SetAttributes[LongRightArrow, HoldRest]

LongRightArrow[obj_, property_] := obj[ToString[property]];
LongRightArrow[obj_, Part[property_, partspec__]] := 
Part[LongRightArrow[obj, property], partspec];
Protect[LongRightArrow];
obj = <|"a" -> {2, 3}, "b" -> 5|>
obj⟶a
obj⟶a[[1]]

<|"a" -> {2, 3}, "b" -> 5|>

{2, 3}
2

Chip Hurst was quicker than I to show the generalization

LongRightArrow[obj_, head_[f_, args__]] := head[LongRightArrow[obj, f], args]

So I'll just take one more step to handle unary postfix operators, such as ! (Factorial). Trivial by replacing args__ with args___:

LongRightArrow[obj_, head_[f_, args___]] := head[LongRightArrow[obj, f], args]

Now

obj⟶a!

{2, 6}

EDIT
Re the comment:

obj⟶a⟶b

is equivalent to

LongRightArrow[obj, a, b]

while the desired behavior is

LongRightArrow[LongRightArrow[obj, a], b]

Well, obviously, that's exactly what we should tell Mathematica, it can't guess that for us.

LongRightArrow[obj_, a_, b__] := LongRightArrow[LongRightArrow[obj, a], b]
obj⟶a⟶b⟶b⟶b⟶b⟶b

 (((((obj⟶a)⟶b)⟶b)⟶b)⟶b)⟶b