Ignored nature because lazy and spreads are limited already; you can use Synchronize if you care.

BDSP Roamer Spread Calculator.cs

void Main()
{
    // Initial state
    // s0 should be s1, s0 from CS
    // s1 should be s3, s2 from CS
    ulong s0 = 0x0123456789ABCDEF;
    ulong s1 = 0x0123456789ABCDEF;

    // Set this for how far you want to search.
    int maxAdvance = 500000;

    var rng = new XorShift128(s0, s1);
    for (int advances = 0; advances < maxAdvance; advances++)
    {
        GetStateRoamer(advances, rng);
        rng.Next();
    }
}

// You can define other methods, fields, classes and namespaces here
private void GetStateRoamer(int advance, XorShift128 rng)
{
    int FlawlessIVs = 3;
    var (s0, s1) = rng.GetState64();
    var output = $"{advance} | {s0:x16} | {s1:x16} |";

    var seed = rng.NextUInt(); // Seed is also the EC.
    output = output + $" {seed:x8} |";

    var xoro = new Xoroshiro128Plus8b(seed); // Feed the seed into a xoroshiro object.
    var fakeTid = xoro.NextUInt();
    var pid = xoro.NextUInt();
    output = output + $" {pid:x8}";

    bool isShiny = false;
    uint shinyXor = 0;
    int TSV = (int)((fakeTid >> 16 ^ (fakeTid & 0xFFFF)) >> 4);
    int PSV = (int)((pid >> 16 ^ (pid & 0xFFFF)) >> 4);
    if (PSV == TSV) // Shiny check vs a fake trainer.
    {
        var upper = (pid >> 16) ^ (fakeTid >> 16);
        shinyXor = (pid & 0xFFFF) ^ (fakeTid & 0xFFFF) ^ upper;
        isShiny = true;
        var shinySymbol = shinyXor == 0 ? "Q" : "T";
    	output = output + $" {shinySymbol} |";
    }
    else
        output = output + "   |";

    int[] ivs = {-1, -1, -1, -1, -1, -1};
    var i = 0;
    while (i < FlawlessIVs)
    {
        var next = xoro.NextUInt(6);
        if (ivs[next] == -1)
        {
            ivs[next] = 31;
            i++;
        }
    }

    var ivstring = "";
    for (i = 0; i < 6; i++)
    {
        if (ivs[i] == -1)
        {
            var next = xoro.NextUInt(32);
            ivs[i] = (int)next;
        }
        ivstring += ivs[i];
        if (i < 5)
            ivstring += "/";
    }

    output = output + $" {ivstring}";

    // Add your filters here.
    if (!isShiny)
        return;
    if (shinyXor != 0)
        return;
    //if (ivs[0] != 31 || ivs[1] != 0 || ivs[2] != 31 || ivs[3] != 31 || ivs[4] != 31 || ivs[5] != 31)
    //    return;
        
    Console.WriteLine(output);
}

Setup is:

1. Download/install LINQPad 7.
2. Download dev build PKHeX.
3. Press F4 in LINQPad and add PKHeX.Core.dll to first tab, and PKHeX.Core to second tab,
4. Change the language at the top to C# program, then copy/paste the script in verbatim.
5. Edit your param (seeds, advances, and filters). The number for Nature can be referenced on Bulbapedia.
6. Click run. Each line should be showing Advances, s0, s1, EC, PID, IVs, Nature.