On Twitter, @RCoderWeb provided a reproducible distill site with custom theme css:
https://github.com/R-CoderDotCom/distill_increase_logo
A comment on this example was:
Hi! I've created a reproducible example but the positioning depends on the image size, that's why you couldn't center the elements properly. You will need to fine-tune transform: translateY(-70%); and top: 25%; on the example.
Here is the example css provided in the repo:
/*-- Additional custom styles --*/
/* Add any additional CSS rules below */
.distill-site-header .logo img {
display: inline-block;
width: 100px;
height: 100px;
max-height: 100px;
}
.distill-site-header {
height: 100px;
}
.distill-site-header .title {
position: relative;
transform: translateY(-70%);
}
.distill-site-header .nav-right {
top: 25%;
position: relative;
}
d-title{
margin-top: 50px;
}
This did work for me, with the experimental tweaking as suggested. 