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I played a new opponent today who had never faced orks and he brought up an issue I'd not considered. I da jumped my SSAG in order to acquire a target, which counts as moving and therefore means that I must subtract 1 from hit rolls.
To counter this, as I have always done, I played More Dakka;

"Use this stratagem before an ORK unit from your army shoots in the shooting phase. Until the end of the phase, that unit's Dakka! Dakka! Dakka! ability triggers on unmodified hit rolls of 5 or 6, instead of 6."

My opponent pointed out that the strategem doesn't negate the subtract 1 to hit for moving a heavy weapon, unlike the DDD which states;

"Each time you make an unmodified hit roll of 6 for an attack with a ranged weapon made by a model in this unit, that hit roll succeeds regardless of any modifiers."

On the next turn, without moving, then DDD would then trigger on 5's and 6's.

So, I think that I may have unintentionally been playing this incorrectly by thinking it was a stratagem that allowed DDD to always trigger on 5+ instead of 6+, regardless of modifier. Have I been mistaken?

Moar Dakka! is commonly used to negate hit penalties, because with it, you automatically hit on an unmodified 5 or 6. As in, if 5 or 6 is on the die, you hit.

Which is why I always used it that way, however the stratagem only seems to trigger on "unmodified" 5 and 6. If I move the heavy weapon, the roll is modified by taking 1 from the die roll. So a 5 becomes a 4 and a 6 becomes a 5.
At that point DDD is triggered by any 6's showing, but the 5s are now 4s so don't count because the stratagem doesn't say "that roll hits regardless of any modifiers", unlike the DDD ability.

RAW, it seems pointless.

I hope it's DDD on 5+ like I have always played it, but this casts doubt on that assertion.

No, you have been playing it correctly and your opponent was incorrect.

Here's the process;

Roll dice.
Count number of unmodified 5s or 6s.
These are your hits.
They also trigger DDD so roll that many dice again.
Count number of unmodified 5s or 6s.
These are also hits.
Job's a good'n.

If you discounted a "natural" 5 that you had rolled (because -1 to hit) you have just modified the roll. DDD and MD specifically work off of unmodified rolls, as you have pointed out.

Don't forget that Dakka^3 isn't just the extra shots, it's also the rule that allows natural 6's to hit regardless of modifiers. So because More Dakka! triggers Dakka^3 on a 5 or 6, that means natural 5's and 6's still hit.

In GW-speak, "unmodified roll" means "the dice roll before modifiers are applied". This is indirectly addressed in the Rulebook FAQ:

Q: If a rule states that an ability triggers on, for example, ‘hit
rolls of 6+’, does this refer to the result of the dice rolls before or
after modifiers are applied?
A: It refers to the final result, after re-rolls and modifiers
(if any) have been applied.
The only exception to this would be abilities that specifically
state, for example, ‘unmodified hit rolls of 6’, or ‘hit rolls of 6
before modifiers are applied.’

 Cheexsta wrote:
In GW-speak, "unmodified roll" means "the dice roll before modifiers are applied". This is indirectly addressed in the Rulebook FAQ:

Q: If a rule states that an ability triggers on, for example, ‘hit
rolls of 6+’, does this refer to the result of the dice rolls before or
after modifiers are applied?
A: It refers to the final result, after re-rolls and modifiers
(if any) have been applied.
The only exception to this would be abilities that specifically
state, for example, ‘unmodified hit rolls of 6’, or ‘hit rolls of 6
before modifiers are applied.’

Thank you, that was what I was looking for.