Damn..... I wish I had $15k to just drop on a collection. This is the perfect collection for me! I sadly didn't start playing until around the 2011 era when you came back, so I've been slowly trying to collect past sets. How I wish I'd played as a kid when Magic was first coming out....
Anyways, enough daydreaming. 
On to some tips.
First, even though you said you don't want to sell singles, don't be surprised if that's still the main advice people give you. It's by far the best way to get maximum value from your collection. But I agree with you -- time is valuable and not replaceable, so sometimes just selling en masse is preferable. However, I might still recommend selling the top 1% of your collection as singles, then sell the rest as one lot. Not only will this get you better value for your high-end cards, it'll also reduce the overall cost of the large lot, making it much more accessible for others and easier for you to move.
But let's say you truly don't want to bother with any single sales and want to move the whole collection....
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We need to be realistic about value. As you already hinted at, Deckbox pricing is not helpful. At most, it shows you the relative value of your cards, helping you pick out those high-end cards if you wanted to. But there's three main things to consider here:
Deckbox values are almost always inflated compared to more competitive marketplaces like TCG Player and eBay. I have found that, as a general rule of thumb, if I subtract about 15% of the Deckbox-listed value, that's pretty close to a more realistic value. Obviously there's exceptions to this in both directions, and that's especially true once you're dealing with older cards. The ONLY reliable price source for old, high-end cards are eBay's sold listings. This is what people are actually paying for the particular card you have, including condition. But to get us in the ballpark, we can just apply my handy 15% rule across the board.
No one pays retail value for bulk. Now, everyone's definition of bulk varies depending on what they deal in. People who deal in $50-$100 cards will probably consider anything under $2 bulk, whereas someone who deals in $500-$2000 cards may not look at anything less than $10-$20. But regardless of where you set the threshold, you have to consider that the majority of the "value" quoted by Deckbox is from bulk. Even if their average price is only 50 cents, 10,000 cards will still claim to be worth $5k!! In reality, most places are only going to pay a penny per card. Maybe if they know there's $2-$5 cards among them, they'll pay more like 5 cents per card. But you're still looking at only $100-$500 for those 10k cards, not $5000.
Finally, if you plan to sell en masse, be prepared to accept only 50%-75% of the collection's value, depending on where you go and how you're paid (for instance, some stores offer higher percents if you get paid in store credit... though I'm guessing that's not something you want, as it seems you're cashing out of the game entirely). That's the price you pay for selling fast. Think of it as the time you didn't spend selling singles.
Given all that, I went through your collection and found the following:
Bulk Value of
threshold Cards high-end Bulk Bulk value Total Value
--------- ----- ---------- ------ ---------- -----------
>= $2 849 $22,018.30 13,732 $ 274.64 $22,292.94
>= $5 401 $20,611.78 14,180 $ 709.00 $21,320.78
>= $10 229 $19,374.62 14,352 $1,435.20 $20,809.82
>= $20 121 $17,871.45 14,460 $2,892.00 $20,763.45
So I first converted all prices to 85% of Deckbox, then used different thresholds to give you some guestimates for different routes you might take.
The way I handled bulk is I priced it per-card at a value equal to 1% of the threshold. So when your bulk threshold is $2, you're getting 0.02 per card, while when the threshold is $10, you're getting 0.10 per card.
Lastly, remember #3 from above. As you can see, your collection's value is somewhere around $21k to $22k, depending on how you proceed. But you're only going to get $11k to $16k, depending on who you're working with.
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So assuming you're cool with getting ~$13k for your collection by selling it all at once, where should you go? Well, individual collectors are probably going to give you more value than stores (remember that stores then need to be able to turn around and make a profit), but they're also riskier to deal with.
The only specific recommendation I can make is Rudy from Alpha Investments (he has a large YouTube channel you can easily find). He has an established public record of being reputable and good to work with (despite a lot of early on hate he received). As one of his patrons, I can attest to the fact that he takes care of his people, no matter what. He'll be particularly interested in your vintage cards, as that's what he deals in (he doesn't have much interest in newer stuff, so you might just sell him your vintage and save the newer part of your collection for another buyer). And if you're game, he might even feature your collection on his channel. Email: AlphaInvestmentsLLC@gmail.com
Can't believe I'm actually recommending him. I'm kinda sick of all the vintage cards getting forever locked away in his vault! LoL. Can't he just let the rest of us have a few of those cards???
Anyways, he's a good guy. Fully support and recommend.
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