I suggest you create a dedicated macro called, say, \tran
to act as the transpose operator. It's no problem to set it up in such a way that its height above the baseline is invariant to what characters may precede it.
If you want to use the \top
symbol to denote the transpose, I would suggest you reduce its size via a \scriptscriptstyle
directive.
Depending on the math font family you use, you want to fine-tune the spacing adjustments made before and after the transpose symbol.

\documentclass{article}
\usepackage{amsmath}
\newcommand{\vect}[1]{\mathbf{#1}}
\newcommand{\vA}{\vect{A}}
\newcommand{\dvect}[1]{\vect{\dot{#1}}}
% "\tran": transpose operator
\newcommand\tran{\mkern-1mu{}_{}^{\scriptscriptstyle\top}\mkern-4mu}
\begin{document}
\begin{align*}
&{_\mathrm{K}}\dvect{\hat{\vA}}^\top \quad {_\mathrm{K}}\dvect{\vA}^\top \quad
{_\mathrm{K}}\vA^\top \quad
\Gamma^{\top}\Gamma \quad H^{\top}H \\
&{_\mathrm{K}}\dvect{\hat{\vA}}\tran \quad
{_\mathrm{K}}\dvect{\vA}\tran \quad
{_\mathrm{K}}\vA\tran \quad
\Gamma\tran \Gamma \quad H\tran H
\end{align*}
\end{document}
Addendum: If you wanted to (a) raise the transpose symbol a bit more relative to the example code above and (b) shift it a bit more to the left (so that it's closer to the symbol that precedes, you might use the following version of the \tran
macro:
\newcommand\tran{\mkern-2mu\raise1.25ex\hbox{$\scriptscriptstyle\top$}\mkern-3.5mu}
Relative to the version shown in the MWE, the symbol is shifted 1mu
(equivalent to one third of a thin-space) more to the left, and it's also placed a bit higher up.
\dvect
to\newcommand{\dvect}[1]{\dot{\vect{#1}}}
seems to have less problem with superscript placement.{}^{\mathrm t\mkern-1.5mu}A
. The\prescript
command frommathtools
can do that too.