"Assuming that the chemical signals are the only way to communicate efficiently".
Well, since after 4 billion years of evolution, we use "chemical signals" I certainly won't fault the idea that they are efficient on the scale of micrometers to meters. A message can be simple (Run!, Duck!, Sex!, Food!) or it can be quite complex (Plans for D-Day invasion, War and Peace, etc., etc.).
Chemical communication excels at the simple, not the complex (at least, not over distances at the meter or kilometer scales (and don't even try for AU scales!)). So, the only obvious communication mode would be "sending letters" or an even closer analogy "messages in bottles".
Currently Earth is ~21 light-seconds from Mars and ~6 from Venus. Those are tremendous distances. Assuming some secretary generated the message and then sent it up to some orbiting platform which then copied the message, encapsulated it, and then broadcast it in the right direction so that there was a near certainty that it would be received by the intended recipient, the unknowns would be:
- mass of a message and container
- the energy requirement to accelerate it (particle accelerator)
- the number of messages sent so that at least one was received along with the
- aiming of the message stream.
Mass Spectrometry is the nearest thing I can think of. It can accelerate 1000 Da peptides (for example) to 50,000+ m/s. This means the journey between Earth and Venus would be 3½ Weeks and Earth to Mars of 3-4 months.
That's one single 'text' message, one-way. It could take years for a typical conversation. If the insects were "advanced", I'd expect them to be smart enough to encode their communications electronically and send them that way.
You'll note that I avoided addressing any of the questions I posed. I see no significant difficulties in creating the message and bottle (the bottle would be the matrix which was ionized to allow acceleration as well as protecting the message from (some) radiation damage in transit.).
I also see no problems in building what would amount to a linear accelerator in orbit above Earth (or planet of your choice). I have no idea how many messages (how much mass) would be required, but I'd assume it to be enormous - on the order of 10s to 1000s of kilograms... but this is something I don't feel I've any relevant experience with, my guess is probably little better than yours.
The aiming of the message stream is also a problem: without actual electronic signals of the Sun's solar wind, etc. there's no way they could accurately aim the message. This would increase the necessary mass sent (in hopes of at least one "lucky" hit) enormously. To do it effectively, they'd need electronic monitoring of solar activity, but if they were already monitoring remote events electronically, they'd have to be morons not to use the same type of electronic signaling for their communications.