You cannot fix the meaning of a single bid in isolation from others.
Based on your 1C including 12-13 balanced hands, I'm assuming that your 1NT opening is 14-16 HCP and that 1D promises an unbalanced hand with 4+ diamonds. If that's not the case, you have imported a gadget that doesn't fit in your system.
The reason for the 1S "transfer to no trump" is to right-side the contract. If responder's heart holding is not positional (Axx or QJT), they want opener's hand to declare. If they have a positional heart stopper (Kxx or AQx, for example), they want the opening lead to come up to their hand. In the first case, responder bids 1S to make opener the declarer. In the second, responder bids some number of no trumps, depending on strength, to make themselves declarer.
Note that 1S can contain any strength of hand, from a desire to play 1NT, to invitational, to game-forcing, to slam-interested. It's important to understand further rebids. If opener breaks the transfer, 2C should show 5+ clubs in an unbalanced hand with less than reversing strength, with 2D and 2S as natural reverses, 2NT as 17-19 with a heart stopper, and 2H as some other forcing hand. If opener accepts the transfer, it's important to understand responder's rebids. Which are weak? Which are invitational? Which are forcing?
For example (and I haven't worked out the full system, so this may be an inferior agreement), you may agree that
1C (1H) 1S; 1NT 2D shows a weak hand with long diamonds. What's the difference, then, between responder bidding 2D initially, 3D initially, or bidding 1S then 3D?
As for a hand with long spades: After
1C (1H), what does 2S show? After
1C (1H) X, what do opener's 1S, 1NT, and 2S rebids show? What about 2C, 2D and 2H? I suggest 1S show 3-card support in a 12-13 balanced hand and 2S shows a hand that would have bid 2S in an uncontested auction starting
1C 1S. I don't have too much experience with this system, so I don't know whether 1NT should promise a stopper and 2C includes balanced minimums, or whether 1NT should be 12-13 balanced without 3 spades and 2C is unbalanced with 5+ clubs.
In any case, you need to decide what all of these sequences show in order to understand how to bid a hand with 6+ spades.