Is parallelling inductors a viable solution?
That is not a viable solution. You are correct that paralleling would allow you to pass more total current, but the effective inductance would be decreased.

The equivalent inductance for parallel inductors is $$L_{equiv}=\Bigl( \frac 1 L_1 + \frac 1 L_2 + ... + \frac 1 L_n  \Bigr) ^{-1}$$

The equivalent inductance for series inductors is $$L_{equiv}=L_1+L_2+...+L_n$$

For series inductors, the equivalent current rating would basically be equal to the lowest rated inductor in the circuit. For example, for a 2A RMS inductor in series with a 1A RMS inductor, the equivalent current rating would be 1A RMS.

For parallel inductors, the (DC) current would be split evenly between them so the total current through the network could be \$I_{total}=nI_{rated}\$ where \$n\$ is the number of inductors paralleled and \$I_{rated}\$ is again the lowest of the current ratings. 

For \$8.2\mu\text{H}=L\$ you would need eight of those inductors to meet your spec. That's two parallel branches each with four series inductors. This would split the 3.5A RMS current evenly between each branch (1.75A RMS in each) and yield an effective inductance of \$(1/2)(4)(8.2\mu\text{H})=(2)(8.2\mu\text{H})=16.4\mu \text{H}\$. I would guess that this approach would not save board space.

Your best bet is probably to find another inductor with a higher current rating. Or as suggested in the comments to Markrages's answer, you could parallel two larger valued inductors. Whichever uses the least space sounds like it would be the best solution.