Answers to cryptic clues:
While on vacation, respectable advisor can...
R_E + A_R = REAR (can)
BID, double definition (a go is a bid/attempt, to tell someone is to bid them)
...King to invade valley in order to obtain fiddle
BB to invade DALE = DABBLE (fiddle)
B,D,R,T,U cannot be zero as they appear as starting digits. I cannot be zero because I×REAR=UCICB is not zero. From RCLEE-RITAT=RBU being a three-digit number we see that C=I+1, so C cannot be zero. From UEDAL-UCICB>0 we see E>C, so E cannot be zero. A cannot be zero because DABB-TTBA=UEDA doesn't end in B. This leaves only one option for zero, which is L.
From UEDA0-UCICB=RC0E we see that 10-B=E, and that (A-1)-C=0 -> A=C+1. Since we know from earlier that C=I+1, that means that I,C,A must be three consecutive digits in ascending order.
DABB-TTBA=UEDA means that B is even (since either B=2A or 10+B=2A). From the last digits of UEDA0-UCICB=RC0E we also see that E is even. And from the last digits of RC0EE-RITAT=RBU we see that T,U are either both even or both odd. If they were both even we'd have too many even digits (L=0, B, E, T, U and at least one of I,C,A). So T,U are both odd.
The placement of I,C,A is restricted now. It can't be 1,2,3 or I×REAR would be REAR. It can't be 2,3,4 or the remaining even digits B,E would be 6,8 and there's no way to make 10-B=E. It can't be 3,4,5 or B would be 0, which is already taken by L. It can't be 5,6,7 or B would be 4, making E=6 which is already taken by C. It can't be 6,7,8 or B would be 6, which is taken by I. And it can't be 7,8,9 or there'd be no room left for E>C. So the only option left is I,C,A = 4,5,6.
6+6=10+B gives B=2, and since we know 10-B=E, we get E=8. All of a sudden it looks like we might know what we'll be spelling here...
From the last subtraction we see 8-T=U or 18-T=U. The only options that work are T,U being 1,7 in some order. So D,R are 3,9 in some order. R cannot be 9 since 2×R86R is a four-digit number. So R=3 and D=9.
To finish off we can just type in 2×3863 into a calculator, giving 7726 meaning T=7. This means U=1, giving the final answer. To get our clues unstuck, we need to get them