Below is what you asked (see below).
First you look what are the trump cards unknown. There are three JD AH 9H. What are the probabilities, with 18 unknown cards in total, for opponents?
1 trump card - 47%
2 trump cards - 16%
3 trump cards - ~1.5%
0 trump cards - 35% (I rounded but needs to add to 100%)
So let's assume you always play the hand correctly by leading JH first followed by the KH to the 2nd trick.
To stop your loner one opponent has to have JD/9D, or JD/AH or AH/9H or all three. Any 2 of the 3 unknown will stop your loner - that 16%. But you have two opponents and that number is doubled 32% probability that your loner will be stopped just by those unknown trumps.
What about that QS lead to the last trump - that is the turned down suit and quite difficult to calculate an EXACT chance it goes through. You partner could have AS or KS or they in combination could be with S3 or buried. And sometimes the opponents get forced with AS/AC, AS/AD, or KS/AC, ect etc. But chance of that going through with 3 off suits is quite high 50 - 60% (estimate, guessing)
So you are looking at being euchred - 3%. I can't believe your statement about getting euchred FREQUENTLY? An opponent has to have 3 trumps?
For a successful loner - 32% get stopped by trump, and 40 - 50% with AS/KS. Those are not additive as could hold at same time but I estimate a loner is successful 30 - 35? Definitely go alone as you will score more points than taking your partner along. All that depends on score as well - how bad do you need a loner? Spades is the turned down suit and favors those critical cards being buried and/or with S3. And it is always more difficult for opponents to stop a loner when they have to decide with three (3) off suits. SWAG on making a loner 30 - 36%. That score way more points than taking your partner along.
Can my partner help me? Yes if he has the JD guarded or AH guarded, with an off suit ace. Or has AS or KS if AS is buried if an opponent only has one trump. But that is less less than is around 40% (estimate, guessing). You can't give exact probabilities on that a march.
I hope that helps. And there might be other opinions but I think I am pretty close and what I would do. Others can jump in and comment.
I know of know chart on probabilities. You would have to learn how to calculate probabilities if interested.
P.S. (I should have also said - that 36% is about stopping you.)
For example consider that each opponent may have just one trump each - 47% x 47% = about 24% of the time; and some times one has 1 and 0 - 47% x 35% = about 12% x 2 = 24% (doubled as 0 & 1 and 1 & 0); and sometimes 0 & 0 - 35% x 35% = ~11% and those add to 24 + 24 + 11 = 64% (without rounding add to about 64%.) Has to add to (64 + 36 =) 100% all probabilities. When that is true then only the AS/KS remains to stop you. Gets complex!
IRISH
Newbe said, "Second of all, I am stuck thinking about a specific hand and the actual probabilities of each outcome. I'm pretty sure I've been euchred going alone on this exact hand in the past, and just want to see the numbers laid out to help me wrap my head around why this is not a good choice.
My Hand:





I am pretty sure a

Is there an easy way to calculate my odds of taking all if I go alone?
Odds of getting at least 3?
Odds of getting Euchred?
Odds of getting all if I bring my partner?
Odds of getting Euchred if I bring my partner?
How much does taking my partner with me actually benefit me?"