SVG Scale without moving location

What I'm trying to do is simple: scale some SVG dots from scale(0) to scale(1) when a sibling element is hovered using vanilla js. They are the red ones in the demo

Here's the basic SVG setup

<?xml version="1.0" encoding="utf-8" ?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN" "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
<svg version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" 
      x="0px" y="0px" viewBox="0 0 720 576" style="enable-background:new 0 0 720 576;" xml:space="preserve">
    <style type="text/css">
        .st3 {
            fill:red;
        }
        * {
            -webkit-transition:.3s;
            transition:.3s;
        }
    </style>
    <g id="Layer_4">
        <!-- Shield -->
        <path class="st8" d="M601,304.7c-32.4-15.4-68.6-24-106.8-24c-40.4,0-78.5,9.6-112.3,26.6c4.9,79.7,41.9,146.7,109.5,187.6
            C559.8,454.1,597,385.6,601,304.7z" />
        <path class="st9" d="M420.1,328.7c2.1-4.7,32.5-23.9,72.5-23.9c39.9,0,73.1,20,75.5,24.3c2.4,4.3,5.7,40-12.7,74.6
                c-19.7,36.9-53.5,50.1-61.8,50.4c-6.4,0.2-41.8-14.3-62.5-51.6C411.5,367.4,418,333.4,420.1,328.7z" />
        <circle class="st10" cx="494.9" cy="373.3" r="35.5" />
    </g>
    <g id="Layer_8">
        <!-- Dots on shield -->
        <circle class="st3" cx="578.8" cy="316.2" r="4.6" />
        <circle class="st3" cx="543.4" cy="346.2" r="4.6" />
        <circle class="st3" cx="505" cy="375.5" r="4.6" />
    </g>
</svg>

The issue is that SVG scales based on the origin location, not the current location, thus when a transform is applied it moves the element in addition to scaling it. I am attempting to fix this situation by translating by the BBox() offset, scaling, then translating back but that only seemed to help and not entirely fix the issue.

var shield = document.getElementById("Layer_4"),
    dots = document.querySelectorAll("#Layer_8 .st3");

toggleTransform(false);

shield.onmouseover = function () { toggleTransform(true); }
shield.onmouseout = function () { toggleTransform(false); }

function toggleTransform(bool) {
    if (!bool) {
        for (var i = 0; i < dots.length; i++) {
            var box = dots[i].getBBox(),
                cx = box.x + box.width / 10,
                cy = box.y + box.height / 10;
            //dots[i].setAttribute("transform", "translate(" + cx + " " + cy + ") scale(0) translate(" + cx + " " + cy + ")");
            dots[i].style.WebkitTransform = "translate(" + cx + "px, " + cy + "px) scale(0) translate(" + -cx + "px, " + -cy + "px)";
        }
    } else {
        for (var i = 0; i < dots.length; i++) {
            var box = dots[i].getBBox(),
                cx = box.x + box.width / 2,
                cy = box.y + box.height / 2;
            //dots[i].setAttribute("transform", "translate(0 0) scale(1) translate(0 0)");
            dots[i].style.WebkitTransform = "translate(0, 0) scale(1) translate(0, 0)";
        }
    }
}

I tried using both setAttribute and CSS's transform (I couldn't get setAttribute to transition, presumably because it's not animatable by CSS) but couldn't get it with either. I've only been testing in Chrome

Anyone have an idea how I can scale, while not moving, red dots?

Here's the demo again if you missed it

Edit

I made a function based on RashFlash's answer to make it quite simple to use and also takes into account offsets and different transform origins

function scaleMe(elem, scaleX = 1, scaleY = 1, newOffsetX = 0, newOffsetY = 0, originX = "center", originY = "center") {
    const bbox = elem.getBBox();
    const cx = bbox.x + (bbox.width / 2);
    const cy = bbox.y + (bbox.height / 2);
    let tx = -cx * (scaleX - 1) + newOffsetX;
    let ty = -cy * (scaleY - 1) + newOffsetY;        
    
    if (originX === "left" || originX === "right") {
        tx = newOffsetX;
    }
    if (originY === "top" || originY === "bottom") {
        ty = newOffsetY;
    }
    
    const scaleStr = `${scaleX},${scaleY}`;
    const translateStr = `${tx}px,${ty}px`;
    
    elem.style.transformOrigin = `${originX} ${originY}`;
    elem.style.transform = `translate(${translateStr}) scale(${scaleStr})`;
}

Updated to work with modern browsers that support transform-box Previously, this approach worked only in Chrome. But spec changes to how transform-origin works, and the addition of transform-box now means that this works in more browsers (currently Chrome, FF, and Opera).

You can actually achieve this effect without JS.

.st3 {
    fill: red;
    -webkit-transform: scale(1);
    -webkit-transform-origin: 50% 50%;
    -webkit-transition:.3s;
    transform: scale(1);
    transform-origin: 50% 50%;
    transition:.3s;
    transform-box: fill-box;
}

#Layer_4:hover + g .st3 {
    -webkit-transform: scale(2);
    -webkit-transform-origin: 50% 50%;
    -webkit-transition:.3s;
    transform: scale(2);
    transform-origin: 50% 50%;
    transition:.3s;
}

Demo here