While the OTG method was already mention and sounds very attractive. I never managed to get it to work with any of the phone I tried. It just never mounted two storage devices at once.

Back when my cameras were using Compact Flash cards, I had the perfect solution which will work for you. It is a portable DVD burner with built-in memory card readers for multiple formats. It can be both battery or A/C powered and the battery lasts for 10 burns in a single charge which gives you 47 GB of backups between recharges. This is ideal since DVDs are incredibly cheap and durable. They have no value to anyone else (so unlikely to be stolen) and you can get backups by duplicating each card into 2 disks. I used to do this, keep one copy with me and mail myself the other. Replication and distribution which is what you want for backups.

Saldy for me, they never updated it to support SDXC cards. So what is left is to backup to an external drive but those are costly. You must buy a $200-300 portable case with card reader, plus the storage inside it. One can use a standard HDD but that is very risky, so you must really go to SSDs which as you may know are costly.

The bottom line is that buying more CF cards will probably be the most cost-effective solution. CF cards are also incredibly sturdy and much less likely to fail than other methods.