This solution is slower than fill curve. Well I didn't compare with fill curve + extrude + normal check, but probably slower anyway. I can produce an artificial case in which this solution is faster, for example 10 nested circles with 20k resolution each (check the file at the end) will make my solution an order of magnitude faster.

You can check previous revision of this answer to see the thought process.

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1. Prepare Geometry - convert splines to Targets. A Target is just a spline converted to mesh and extruded up, so that raycasting can be used on it. Normals are recalculated to point outside. Also convert vertical edge of this geometry to points, which will hold ray data, therefore the points are called Rays.

2. Make Gun Range - The Targets together are called Target Level, because each set of mesh islands has to be duplicated for each spline ("geometry explosion") because it is going to be duplicated in a moment, with each duplicate on a separate $z$ position (separate floor or level). All duplicates together I call Gun Range.

3. Extended Raycast - contains the Raycast node and some basic logic and data reading/storing that otherwise would repeat later in the node tree (inside the repeat zone), but also to keep the setup as simple as possible. Notice how they rays are moved vertically, each having its own level.

4. Kill Targets - imagine going horizontally through a (somehow closed) sinusoid, you would keep entering/leaving the same spline. However you only need to hit each curve once to determine if it's inside it, based on normal. So once the Target is hit, it is removed from the Gun Range, making sure you don't hit it again. This also makes the repeat zone very manageable, because you know you can hit at most each spline once, so the number of iterations can be set to the number of splines. The deletion also means you don't need the classic offset by normal scaled by 0.001 to not hit the same Target again.

5. Delete Geometry - remove Ray data that never hit anything, because it doesn't contain any useful information.

6. Store first_exit for your Rays, the calculated value is -1 if there wasn't an exit.

7. Repeat Zone: do raycasts, notice this time position isn't passed - that's because Extended Raycast moves the point to the hit position internally. Kill Targets works the same way, storing first_exit makes sure to store it only on points that haven't yet encountered an exit, and rays that missed are separated and moved to Escaped Rays as finished job; thanks to this, most iterations do nothing, because for most inputs all rays will escape on like 10% of first iterations, and then the rest of iterations does nothing (consider adding 3 switches with a check of domain size to further optimize).

8. If you unmute the Subtract node, then Join Geometry also has to be unmuted because then theoretically some rays could hit all splines and so they may have not "escaped" yet.

9. Map Values does the usual geonodes logic to read calculated data from rays and move it onto the splines.

The algorithm assumes all splines are cyclic, so remove non-cyclic splines before using it.

Prepare Geometry

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I'm renaming spline_i to ray_i just for readability, so you're less likely to confuse a context in which they are evaluated. In general it should be easier to understand the setup if you keep in mind those two, as well as level and Index in spline context, are equivalent.

Make Gun Range

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Notice the spline_i = level removal, because a ray starting at a particular spline doesn't want to hit its own spline. Remember what I said about Subtract and Join Geometry nodes? Actually you can unmute just the former, or unmute both and subtract $2$ instead.

Extended Raycast

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⚠ The Position input has to be set to default to a position in the numbers panel!

Also, the exit_count could just be a boolean exit_count_odd, and instead of adding to it, you could just "boolean math: NOT" it, as that's all what we care about if the number of exits is even or odd.

Kill Targets

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Pink Mapping: For those rays that missed, move them (the points) to $<0, 0, ray_i>$. You kind of don't have to do that, you could use "Transform Geometry" to scale to 0 on $xy$ axes, and then translate down by $0.5$ for the same effect.

Brown mapping: rays that didn't miss: move them like in the pink mapping, but also set $x$ to Target (spline_i) that was hit.

This way for missed rays you can remove entire level, and for other rays only the Target that was hit.

Map Values

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Delete rays that have an even number of exits, because the first exit of those is not the filling pair. For the rest again use the mapping by position, setting their position to their ray_i. Then for each spline, check if it has a ray-point sitting on it's spline index. If not, it's an outside spline of a filling pair, or a spline without a pair. In such case just set the ID to the index. Otherwise it's an internal spline of a filling pair, so read from the found point the first_exit which holds the index of the external spline of the pair.

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Blend 4.3.2

Some further ideas

Maybe you can remove entire level on finding the first exit curve. This should make raycasting much faster, but then you would need to do more mapping magic at the end to figure out the evenness. I kind of hinted in the first revision how that could be done...