Вы можете сделать это с display: flex;
Попробуйте это:
@media screen and (min-width: 769px){
.site-header .grid, .site-header .grid--rev, .site-header .grid--full {
display: flex;
width: 100%;
align-items: center;
justify-content: center;
}
.site-header .grid>.grid__item, .site-header .grid--rev>.grid__item, .site-header .grid--full>.grid__item {
/* float: none; */
/* display: table-cell; */
/* vertical-align: middle; */
width: 60%;
}
}
.grid__item.post-large--one-third.post-large--display-table-cell { order: 2; }
.grid__item.post-large--two-thirds.post-large--display-table-cell.medium-down--hide {
width: 40%;
display: flex;
order: 1;
}
Это результат :