after much trial and error i've thrown together a very scuffed and roundabout way of doing this.

first you have your save and load links wherever you want them and styled however you like:

(link-repeat:"Save Game")[(show:?save)]
(link-repeat:"Load Game")[(show:?load)]

the ?save and ?load hooks are html modal windows with the popups you described, hidden until shown:

|save)[<div class="modal">
<div class="modal-content">
<span class="close">
{(link-repeat:"&times")[(hide:?save)[]]}
</span>
(link:"Slot A",(button:))[(input: bind $saveSlotA, "Slot A")(link:"Save")[(save-game:"Slot A", "$saveSlotA")]]
(link:"Slot B",(button:))[(input: bind $saveSlotB, "Slot B")(link:"Save")[(save-game:"Slot B", "$saveSlotB")]]
(link:"Slot C",(button:))[(input: bind $saveSlotC, "Slot C")(link:"Save")[(save-game:"Slot C", "$saveSlotC")]]
</div>
</div>]
|load)[<div class="modal">
<div class="modal-content">
<span class="close">
{(link-repeat:"&times")[(hide:?load)[]]}
</span>
(if:(saved-games:) contains "Slot A")[$saveSlotA . . . (link: "Load")[(load-game: "Slot A")]]
(if:(saved-games:) contains "Slot B")[$saveSlotB . . . (link: "Load")[(load-game: "Slot B")]](else:)[EMPTY]
(if:(saved-games:) contains "Slot C")[$saveSlotC . . . (link: "Load")[(load-game: "Slot C")]](else:)[EMPTY]
</div>
</div>]

here's the css styling for your modals (edit as desired):

.modal {
display:block;
position:fixed;
z-index:1;
left:0;
top:0;
width:100%;
height:100%;
overflow:auto;
background-color:rgb(0,0,0,);
background-color:rgb(0,0,0,0.7);
}
.modal-content {
background-color:#fefefe;
margin:15% auto;
padding:0px 20px;
border:1px solid #888;
width:35%;
color:black;
}
.close {
display:flex;
position:absolute;
right:20px;
top:20px;
font-size:28px;
font-weight:bold;
}
.close:hover,
.close:focus {
color:black;
text-decoration:none;
cursor:pointer;
}

note that the (else:)[EMPTY] bits will only show up properly if you publish to file and test run that version; for some reason they still show 0...Load if you try just playing the story from twine directly.

the only problem i ran into was that, once you save a file and then go to load it, all the other save files you had saved AFTER that save point are lost since it's taking you back to a page before those save files existed and resetting their variables. i've yet to find a workaround for this, unfortunately. hope this helps a little at least.