You might be able to do something like that by putting the big logo in a custom header (admin>customize>css/html/new). Add a header to the ‘Header’ section of the editor:
<div class="wrap brand-header">
<a href="<!-- your forum url -->">
<img class="brand-logo" src="<!-- link to big logo -->">
</a>
</div>
You could add some css to hide the regular sized forum logo until the custom header has scrolled out of view:
.brand-header .brand-logo {
/* this moves it down a bit, this could be improved */
position: relative;
top: 25px;
z-index: 1200;
}
/* hides the site logo when the custom header is in view */
.d-header #site-logo {
display: none;
}
/* displays the site logo now that the custom header has scrolled out of view */
.docked .d-header #site-logo {
display: inline;
}
This works, but is barely tested. Use at your own risk.